TSTP Solution File: PLA016-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PLA016-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:39:55 EDT 2022
% Result : Unsatisfiable 25.81s 16.93s
% Output : Proof 25.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PLA016-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.31 % Computer : n001.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Fri Sep 2 17:35:08 EDT 2022
% 0.12/0.31 % CPUTime :
% 0.12/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.32 Usage: tptp [options] [-file:]file
% 0.12/0.32 -h, -? prints this message.
% 0.12/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.32 -m, -model generate model.
% 0.12/0.32 -p, -proof generate proof.
% 0.12/0.32 -c, -core generate unsat core of named formulas.
% 0.12/0.32 -st, -statistics display statistics.
% 0.12/0.32 -t:timeout set timeout (in second).
% 0.12/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.32 -<param>:<value> configuration parameter and value.
% 0.12/0.32 -o:<output-file> file to place output in.
% 25.81/16.93 % SZS status Unsatisfiable
% 25.81/16.93 % SZS output start Proof
% 25.81/16.93 tff(holds_type, type, (
% 25.81/16.93 holds: ( $i * $i ) > $o)).
% 25.81/16.93 tff(do_type, type, (
% 25.81/16.93 do: ( $i * $i ) > $i)).
% 25.81/16.93 tff(s0_type, type, (
% 25.81/16.93 s0: $i)).
% 25.81/16.93 tff(pickup_type, type, (
% 25.81/16.93 pickup: $i > $i)).
% 25.81/16.93 tff(c_type, type, (
% 25.81/16.93 c: $i)).
% 25.81/16.93 tff(putdown_type, type, (
% 25.81/16.93 putdown: ( $i * $i ) > $i)).
% 25.81/16.93 tff(table_type, type, (
% 25.81/16.93 table: $i)).
% 25.81/16.93 tff(a_type, type, (
% 25.81/16.93 a: $i)).
% 25.81/16.93 tff(d_type, type, (
% 25.81/16.93 d: $i)).
% 25.81/16.93 tff(on_type, type, (
% 25.81/16.93 on: ( $i * $i ) > $i)).
% 25.81/16.93 tff(holding_type, type, (
% 25.81/16.93 holding: $i > $i)).
% 25.81/16.93 tff(clear_type, type, (
% 25.81/16.93 clear: $i > $i)).
% 25.81/16.93 tff(empty_type, type, (
% 25.81/16.93 empty: $i)).
% 25.81/16.93 tff(differ_type, type, (
% 25.81/16.93 differ: ( $i * $i ) > $o)).
% 25.81/16.93 tff(1,assumption,(~holds(clear(d), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))), introduced(assumption)).
% 25.81/16.93 tff(2,assumption,(~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))), introduced(assumption)).
% 25.81/16.93 tff(3,plain,
% 25.81/16.93 (holds(empty, s0) <=> holds(empty, s0)),
% 25.81/16.93 inference(rewrite,[status(thm)],[])).
% 25.81/16.93 tff(4,axiom,(holds(empty, s0)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','initial_state8')).
% 25.81/16.93 tff(5,plain,
% 25.81/16.93 (holds(empty, s0)),
% 25.81/16.93 inference(modus_ponens,[status(thm)],[4, 3])).
% 25.81/16.93 tff(6,plain,
% 25.81/16.93 (holds(clear(c), s0) <=> holds(clear(c), s0)),
% 25.81/16.93 inference(rewrite,[status(thm)],[])).
% 25.81/16.93 tff(7,axiom,(holds(clear(c), s0)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','initial_state7')).
% 25.81/16.93 tff(8,plain,
% 25.81/16.93 (holds(clear(c), s0)),
% 25.81/16.93 inference(modus_ponens,[status(thm)],[7, 6])).
% 25.81/16.93 tff(9,plain,
% 25.81/16.93 (holds(on(c, d), s0) <=> holds(on(c, d), s0)),
% 25.81/16.93 inference(rewrite,[status(thm)],[])).
% 25.81/16.93 tff(10,axiom,(holds(on(c, d), s0)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','initial_state3')).
% 25.81/16.93 tff(11,plain,
% 25.81/16.93 (holds(on(c, d), s0)),
% 25.81/16.93 inference(modus_ponens,[status(thm)],[10, 9])).
% 25.81/16.93 tff(12,plain,
% 25.81/16.93 (^[Y: $i, State: $i, X: $i] : refl(((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State))) <=> ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State))))),
% 25.81/16.93 inference(bind,[status(th)],[])).
% 25.81/16.93 tff(13,plain,
% 25.81/16.93 (![Y: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State))) <=> ![Y: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))),
% 25.81/16.93 inference(quant_intro,[status(thm)],[12])).
% 25.81/16.93 tff(14,plain,
% 25.81/16.93 (![Y: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State))) <=> ![Y: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))),
% 25.81/16.93 inference(rewrite,[status(thm)],[])).
% 25.81/16.93 tff(15,plain,
% 25.81/16.93 (^[Y: $i, State: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((holds(clear(Y), do(pickup(X), State)) | (~holds(on(X, Y), State))) <=> ((~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))), (((holds(clear(Y), do(pickup(X), State)) | (~holds(on(X, Y), State))) | (~holds(clear(X), State))) <=> (((~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State))) | (~holds(clear(X), State))))), rewrite((((~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State))) | (~holds(clear(X), State))) <=> ((~holds(clear(X), State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))), (((holds(clear(Y), do(pickup(X), State)) | (~holds(on(X, Y), State))) | (~holds(clear(X), State))) <=> ((~holds(clear(X), State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State))))), ((((holds(clear(Y), do(pickup(X), State)) | (~holds(on(X, Y), State))) | (~holds(clear(X), State))) | (~holds(empty, State))) <=> (((~holds(clear(X), State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State))) | (~holds(empty, State))))), rewrite((((~holds(clear(X), State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State))) | (~holds(empty, State))) <=> ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))), ((((holds(clear(Y), do(pickup(X), State)) | (~holds(on(X, Y), State))) | (~holds(clear(X), State))) | (~holds(empty, State))) <=> ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))))),
% 25.81/16.93 inference(bind,[status(th)],[])).
% 25.81/16.93 tff(16,plain,
% 25.81/16.93 (![Y: $i, State: $i, X: $i] : (((holds(clear(Y), do(pickup(X), State)) | (~holds(on(X, Y), State))) | (~holds(clear(X), State))) | (~holds(empty, State))) <=> ![Y: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))),
% 25.81/16.93 inference(quant_intro,[status(thm)],[15])).
% 25.81/16.93 tff(17,axiom,(![Y: $i, State: $i, X: $i] : (((holds(clear(Y), do(pickup(X), State)) | (~holds(on(X, Y), State))) | (~holds(clear(X), State))) | (~holds(empty, State)))), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-0.ax','pickup_2')).
% 25.81/16.93 tff(18,plain,
% 25.81/16.93 (![Y: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))),
% 25.81/16.93 inference(modus_ponens,[status(thm)],[17, 16])).
% 25.81/16.93 tff(19,plain,
% 25.81/16.93 (![Y: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))),
% 25.81/16.93 inference(modus_ponens,[status(thm)],[18, 14])).
% 25.81/16.93 tff(20,plain,(
% 25.81/16.93 ![Y: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))),
% 25.81/16.93 inference(skolemize,[status(sab)],[19])).
% 25.81/16.93 tff(21,plain,
% 25.81/16.93 (![Y: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))),
% 25.81/16.93 inference(modus_ponens,[status(thm)],[20, 13])).
% 25.81/16.93 tff(22,plain,
% 25.81/16.93 (((~![Y: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))) | ((~holds(empty, s0)) | (~holds(clear(c), s0)) | (~holds(on(c, d), s0)) | holds(clear(d), do(pickup(c), s0)))) <=> ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))) | (~holds(empty, s0)) | (~holds(clear(c), s0)) | (~holds(on(c, d), s0)) | holds(clear(d), do(pickup(c), s0)))),
% 25.81/16.93 inference(rewrite,[status(thm)],[])).
% 25.81/16.93 tff(23,plain,
% 25.81/16.93 (((~holds(clear(c), s0)) | (~holds(empty, s0)) | (~holds(on(c, d), s0)) | holds(clear(d), do(pickup(c), s0))) <=> ((~holds(empty, s0)) | (~holds(clear(c), s0)) | (~holds(on(c, d), s0)) | holds(clear(d), do(pickup(c), s0)))),
% 25.81/16.93 inference(rewrite,[status(thm)],[])).
% 25.81/16.93 tff(24,plain,
% 25.81/16.93 (((~![Y: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))) | ((~holds(clear(c), s0)) | (~holds(empty, s0)) | (~holds(on(c, d), s0)) | holds(clear(d), do(pickup(c), s0)))) <=> ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))) | ((~holds(empty, s0)) | (~holds(clear(c), s0)) | (~holds(on(c, d), s0)) | holds(clear(d), do(pickup(c), s0))))),
% 25.81/16.93 inference(monotonicity,[status(thm)],[23])).
% 25.81/16.93 tff(25,plain,
% 25.81/16.93 (((~![Y: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))) | ((~holds(clear(c), s0)) | (~holds(empty, s0)) | (~holds(on(c, d), s0)) | holds(clear(d), do(pickup(c), s0)))) <=> ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))) | (~holds(empty, s0)) | (~holds(clear(c), s0)) | (~holds(on(c, d), s0)) | holds(clear(d), do(pickup(c), s0)))),
% 25.81/16.93 inference(transitivity,[status(thm)],[24, 22])).
% 25.81/16.93 tff(26,plain,
% 25.81/16.93 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))) | ((~holds(clear(c), s0)) | (~holds(empty, s0)) | (~holds(on(c, d), s0)) | holds(clear(d), do(pickup(c), s0)))),
% 25.81/16.93 inference(quant_inst,[status(thm)],[])).
% 25.81/16.93 tff(27,plain,
% 25.81/16.93 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~holds(empty, State)) | (~holds(on(X, Y), State)) | holds(clear(Y), do(pickup(X), State)))) | (~holds(empty, s0)) | (~holds(clear(c), s0)) | (~holds(on(c, d), s0)) | holds(clear(d), do(pickup(c), s0))),
% 25.81/16.93 inference(modus_ponens,[status(thm)],[26, 25])).
% 25.81/16.93 tff(28,plain,
% 25.81/16.93 (holds(clear(d), do(pickup(c), s0))),
% 25.81/16.93 inference(unit_resolution,[status(thm)],[27, 21, 11, 8, 5])).
% 25.81/16.93 tff(29,plain,
% 25.81/16.93 (differ(d, table) <=> differ(d, table)),
% 25.81/16.93 inference(rewrite,[status(thm)],[])).
% 25.81/16.93 tff(30,axiom,(differ(d, table)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','differ_d_table')).
% 25.81/16.93 tff(31,plain,
% 25.81/16.93 (differ(d, table)),
% 25.81/16.93 inference(modus_ponens,[status(thm)],[30, 29])).
% 25.81/16.94 tff(32,plain,
% 25.81/16.94 (^[Z: $i, Y: $i, State: $i, X: $i] : refl(((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State))) <=> ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State))))),
% 25.81/16.94 inference(bind,[status(th)],[])).
% 25.81/16.94 tff(33,plain,
% 25.81/16.94 (![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State))) <=> ![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 25.81/16.94 inference(quant_intro,[status(thm)],[32])).
% 25.81/16.94 tff(34,plain,
% 25.81/16.94 (![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State))) <=> ![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(35,plain,
% 25.81/16.94 (^[Z: $i, Y: $i, State: $i, X: $i] : trans(monotonicity(rewrite((holds(clear(Z), do(putdown(X, Y), State)) | (~holds(clear(Z), State))) <=> ((~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))), (((holds(clear(Z), do(putdown(X, Y), State)) | (~holds(clear(Z), State))) | (~differ(Z, Y))) <=> (((~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State))) | (~differ(Z, Y))))), rewrite((((~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State))) | (~differ(Z, Y))) <=> ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))), (((holds(clear(Z), do(putdown(X, Y), State)) | (~holds(clear(Z), State))) | (~differ(Z, Y))) <=> ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))))),
% 25.81/16.94 inference(bind,[status(th)],[])).
% 25.81/16.94 tff(36,plain,
% 25.81/16.94 (![Z: $i, Y: $i, State: $i, X: $i] : ((holds(clear(Z), do(putdown(X, Y), State)) | (~holds(clear(Z), State))) | (~differ(Z, Y))) <=> ![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 25.81/16.94 inference(quant_intro,[status(thm)],[35])).
% 25.81/16.94 tff(37,axiom,(![Z: $i, Y: $i, State: $i, X: $i] : ((holds(clear(Z), do(putdown(X, Y), State)) | (~holds(clear(Z), State))) | (~differ(Z, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-0.ax','putdown_5')).
% 25.81/16.94 tff(38,plain,
% 25.81/16.94 (![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[37, 36])).
% 25.81/16.94 tff(39,plain,
% 25.81/16.94 (![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[38, 34])).
% 25.81/16.94 tff(40,plain,(
% 25.81/16.94 ![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 25.81/16.94 inference(skolemize,[status(sab)],[39])).
% 25.81/16.94 tff(41,plain,
% 25.81/16.94 (![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[40, 33])).
% 25.81/16.94 tff(42,plain,
% 25.81/16.94 (((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | ((~differ(d, table)) | (~holds(clear(d), do(pickup(c), s0))) | holds(clear(d), do(putdown(c, table), do(pickup(c), s0))))) <=> ((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | (~differ(d, table)) | (~holds(clear(d), do(pickup(c), s0))) | holds(clear(d), do(putdown(c, table), do(pickup(c), s0))))),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(43,plain,
% 25.81/16.94 ((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | ((~differ(d, table)) | (~holds(clear(d), do(pickup(c), s0))) | holds(clear(d), do(putdown(c, table), do(pickup(c), s0))))),
% 25.81/16.94 inference(quant_inst,[status(thm)],[])).
% 25.81/16.94 tff(44,plain,
% 25.81/16.94 ((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | (~differ(d, table)) | (~holds(clear(d), do(pickup(c), s0))) | holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[43, 42])).
% 25.81/16.94 tff(45,plain,
% 25.81/16.94 ($false),
% 25.81/16.94 inference(unit_resolution,[status(thm)],[44, 41, 31, 28, 2])).
% 25.81/16.94 tff(46,plain,(holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))), inference(lemma,lemma(discharge,[]))).
% 25.81/16.94 tff(47,plain,
% 25.81/16.94 (differ(a, d) <=> differ(a, d)),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(48,axiom,(differ(a, d)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','differ_a_d')).
% 25.81/16.94 tff(49,plain,
% 25.81/16.94 (differ(a, d)),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[48, 47])).
% 25.81/16.94 tff(50,plain,
% 25.81/16.94 (^[Y: $i, X: $i] : refl(((~differ(Y, X)) | differ(X, Y)) <=> ((~differ(Y, X)) | differ(X, Y)))),
% 25.81/16.94 inference(bind,[status(th)],[])).
% 25.81/16.94 tff(51,plain,
% 25.81/16.94 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y)) <=> ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 25.81/16.94 inference(quant_intro,[status(thm)],[50])).
% 25.81/16.94 tff(52,plain,
% 25.81/16.94 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y)) <=> ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(53,plain,
% 25.81/16.94 (^[Y: $i, X: $i] : rewrite((differ(X, Y) | (~differ(Y, X))) <=> ((~differ(Y, X)) | differ(X, Y)))),
% 25.81/16.94 inference(bind,[status(th)],[])).
% 25.81/16.94 tff(54,plain,
% 25.81/16.94 (![Y: $i, X: $i] : (differ(X, Y) | (~differ(Y, X))) <=> ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 25.81/16.94 inference(quant_intro,[status(thm)],[53])).
% 25.81/16.94 tff(55,axiom,(![Y: $i, X: $i] : (differ(X, Y) | (~differ(Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','symmetry_of_differ')).
% 25.81/16.94 tff(56,plain,
% 25.81/16.94 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[55, 54])).
% 25.81/16.94 tff(57,plain,
% 25.81/16.94 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[56, 52])).
% 25.81/16.94 tff(58,plain,(
% 25.81/16.94 ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 25.81/16.94 inference(skolemize,[status(sab)],[57])).
% 25.81/16.94 tff(59,plain,
% 25.81/16.94 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[58, 51])).
% 25.81/16.94 tff(60,plain,
% 25.81/16.94 (((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | ((~differ(a, d)) | differ(d, a))) <=> ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | (~differ(a, d)) | differ(d, a))),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(61,plain,
% 25.81/16.94 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | ((~differ(a, d)) | differ(d, a))),
% 25.81/16.94 inference(quant_inst,[status(thm)],[])).
% 25.81/16.94 tff(62,plain,
% 25.81/16.94 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | (~differ(a, d)) | differ(d, a)),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[61, 60])).
% 25.81/16.94 tff(63,plain,
% 25.81/16.94 (differ(d, a)),
% 25.81/16.94 inference(unit_resolution,[status(thm)],[62, 59, 49])).
% 25.81/16.94 tff(64,plain,
% 25.81/16.94 (^[Z: $i, State: $i, X: $i] : refl(((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State))) <=> ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State))))),
% 25.81/16.94 inference(bind,[status(th)],[])).
% 25.81/16.94 tff(65,plain,
% 25.81/16.94 (![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State))) <=> ![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 25.81/16.94 inference(quant_intro,[status(thm)],[64])).
% 25.81/16.94 tff(66,plain,
% 25.81/16.94 (![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State))) <=> ![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(67,plain,
% 25.81/16.94 (^[Z: $i, State: $i, X: $i] : trans(monotonicity(rewrite((holds(clear(X), do(pickup(Z), State)) | (~holds(clear(X), State))) <=> ((~holds(clear(X), State)) | holds(clear(X), do(pickup(Z), State)))), (((holds(clear(X), do(pickup(Z), State)) | (~holds(clear(X), State))) | (~differ(X, Z))) <=> (((~holds(clear(X), State)) | holds(clear(X), do(pickup(Z), State))) | (~differ(X, Z))))), rewrite((((~holds(clear(X), State)) | holds(clear(X), do(pickup(Z), State))) | (~differ(X, Z))) <=> ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))), (((holds(clear(X), do(pickup(Z), State)) | (~holds(clear(X), State))) | (~differ(X, Z))) <=> ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))))),
% 25.81/16.94 inference(bind,[status(th)],[])).
% 25.81/16.94 tff(68,plain,
% 25.81/16.94 (![Z: $i, State: $i, X: $i] : ((holds(clear(X), do(pickup(Z), State)) | (~holds(clear(X), State))) | (~differ(X, Z))) <=> ![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 25.81/16.94 inference(quant_intro,[status(thm)],[67])).
% 25.81/16.94 tff(69,axiom,(![Z: $i, State: $i, X: $i] : ((holds(clear(X), do(pickup(Z), State)) | (~holds(clear(X), State))) | (~differ(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-0.ax','pickup_4')).
% 25.81/16.94 tff(70,plain,
% 25.81/16.94 (![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[69, 68])).
% 25.81/16.94 tff(71,plain,
% 25.81/16.94 (![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[70, 66])).
% 25.81/16.94 tff(72,plain,(
% 25.81/16.94 ![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 25.81/16.94 inference(skolemize,[status(sab)],[71])).
% 25.81/16.94 tff(73,plain,
% 25.81/16.94 (![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[72, 65])).
% 25.81/16.94 tff(74,plain,
% 25.81/16.94 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~differ(d, a)) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(d), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~differ(d, a)) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(d), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(75,plain,
% 25.81/16.94 (((~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(d, a)) | holds(clear(d), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) <=> ((~differ(d, a)) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(d), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(76,plain,
% 25.81/16.94 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(d, a)) | holds(clear(d), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~differ(d, a)) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(d), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))),
% 25.81/16.94 inference(monotonicity,[status(thm)],[75])).
% 25.81/16.94 tff(77,plain,
% 25.81/16.94 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(d, a)) | holds(clear(d), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~differ(d, a)) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(d), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))),
% 25.81/16.94 inference(transitivity,[status(thm)],[76, 74])).
% 25.81/16.94 tff(78,plain,
% 25.81/16.94 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(d, a)) | holds(clear(d), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))),
% 25.81/16.94 inference(quant_inst,[status(thm)],[])).
% 25.81/16.94 tff(79,plain,
% 25.81/16.94 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~differ(d, a)) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(d), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[78, 77])).
% 25.81/16.94 tff(80,plain,
% 25.81/16.94 ($false),
% 25.81/16.94 inference(unit_resolution,[status(thm)],[79, 73, 63, 46, 1])).
% 25.81/16.94 tff(81,plain,(holds(clear(d), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))), inference(lemma,lemma(discharge,[]))).
% 25.81/16.94 tff(82,assumption,(~holds(clear(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))), introduced(assumption)).
% 25.81/16.94 tff(83,plain,
% 25.81/16.94 (differ(c, d) <=> differ(c, d)),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(84,axiom,(differ(c, d)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','differ_c_d')).
% 25.81/16.94 tff(85,plain,
% 25.81/16.94 (differ(c, d)),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[84, 83])).
% 25.81/16.94 tff(86,plain,
% 25.81/16.94 (((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | ((~differ(c, d)) | differ(d, c))) <=> ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | (~differ(c, d)) | differ(d, c))),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(87,plain,
% 25.81/16.94 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | ((~differ(c, d)) | differ(d, c))),
% 25.81/16.94 inference(quant_inst,[status(thm)],[])).
% 25.81/16.94 tff(88,plain,
% 25.81/16.94 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | (~differ(c, d)) | differ(d, c)),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[87, 86])).
% 25.81/16.94 tff(89,plain,
% 25.81/16.94 (differ(d, c)),
% 25.81/16.94 inference(unit_resolution,[status(thm)],[88, 59, 85])).
% 25.81/16.94 tff(90,plain,
% 25.81/16.94 (((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | ((~differ(d, c)) | (~holds(clear(d), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | holds(clear(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))) <=> ((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | (~differ(d, c)) | (~holds(clear(d), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | holds(clear(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(91,plain,
% 25.81/16.94 ((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | ((~differ(d, c)) | (~holds(clear(d), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | holds(clear(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))),
% 25.81/16.94 inference(quant_inst,[status(thm)],[])).
% 25.81/16.94 tff(92,plain,
% 25.81/16.94 ((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | (~differ(d, c)) | (~holds(clear(d), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | holds(clear(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[91, 90])).
% 25.81/16.94 tff(93,plain,
% 25.81/16.94 ($false),
% 25.81/16.94 inference(unit_resolution,[status(thm)],[92, 41, 89, 82, 81])).
% 25.81/16.94 tff(94,plain,(holds(clear(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))), inference(lemma,lemma(discharge,[]))).
% 25.81/16.94 tff(95,assumption,(~holds(clear(a), do(putdown(c, table), do(pickup(c), s0)))), introduced(assumption)).
% 25.81/16.94 tff(96,assumption,(~holds(clear(a), do(pickup(c), s0))), introduced(assumption)).
% 25.81/16.94 tff(97,plain,
% 25.81/16.94 (holds(clear(a), s0) <=> holds(clear(a), s0)),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(98,axiom,(holds(clear(a), s0)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','initial_state5')).
% 25.81/16.94 tff(99,plain,
% 25.81/16.94 (holds(clear(a), s0)),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[98, 97])).
% 25.81/16.94 tff(100,plain,
% 25.81/16.94 (differ(a, c) <=> differ(a, c)),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(101,axiom,(differ(a, c)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','differ_a_c')).
% 25.81/16.94 tff(102,plain,
% 25.81/16.94 (differ(a, c)),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[101, 100])).
% 25.81/16.94 tff(103,plain,
% 25.81/16.94 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(a), s0)) | (~differ(a, c)) | holds(clear(a), do(pickup(c), s0)))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~holds(clear(a), s0)) | (~differ(a, c)) | holds(clear(a), do(pickup(c), s0)))),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(104,plain,
% 25.81/16.94 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(a), s0)) | (~differ(a, c)) | holds(clear(a), do(pickup(c), s0)))),
% 25.81/16.94 inference(quant_inst,[status(thm)],[])).
% 25.81/16.94 tff(105,plain,
% 25.81/16.94 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~holds(clear(a), s0)) | (~differ(a, c)) | holds(clear(a), do(pickup(c), s0))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[104, 103])).
% 25.81/16.94 tff(106,plain,
% 25.81/16.94 ($false),
% 25.81/16.94 inference(unit_resolution,[status(thm)],[105, 73, 102, 99, 96])).
% 25.81/16.94 tff(107,plain,(holds(clear(a), do(pickup(c), s0))), inference(lemma,lemma(discharge,[]))).
% 25.81/16.94 tff(108,plain,
% 25.81/16.94 (differ(a, table) <=> differ(a, table)),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(109,axiom,(differ(a, table)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','differ_a_table')).
% 25.81/16.94 tff(110,plain,
% 25.81/16.94 (differ(a, table)),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[109, 108])).
% 25.81/16.94 tff(111,plain,
% 25.81/16.94 (((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | ((~differ(a, table)) | (~holds(clear(a), do(pickup(c), s0))) | holds(clear(a), do(putdown(c, table), do(pickup(c), s0))))) <=> ((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | (~differ(a, table)) | (~holds(clear(a), do(pickup(c), s0))) | holds(clear(a), do(putdown(c, table), do(pickup(c), s0))))),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(112,plain,
% 25.81/16.94 ((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | ((~differ(a, table)) | (~holds(clear(a), do(pickup(c), s0))) | holds(clear(a), do(putdown(c, table), do(pickup(c), s0))))),
% 25.81/16.94 inference(quant_inst,[status(thm)],[])).
% 25.81/16.94 tff(113,plain,
% 25.81/16.94 ((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | (~differ(a, table)) | (~holds(clear(a), do(pickup(c), s0))) | holds(clear(a), do(putdown(c, table), do(pickup(c), s0)))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[112, 111])).
% 25.81/16.94 tff(114,plain,
% 25.81/16.94 ($false),
% 25.81/16.94 inference(unit_resolution,[status(thm)],[113, 41, 110, 107, 95])).
% 25.81/16.94 tff(115,plain,(holds(clear(a), do(putdown(c, table), do(pickup(c), s0)))), inference(lemma,lemma(discharge,[]))).
% 25.81/16.94 tff(116,assumption,(~holds(clear(table), do(pickup(c), s0))), introduced(assumption)).
% 25.81/16.94 tff(117,plain,
% 25.81/16.94 (^[State: $i] : refl(holds(clear(table), State) <=> holds(clear(table), State))),
% 25.81/16.94 inference(bind,[status(th)],[])).
% 25.81/16.94 tff(118,plain,
% 25.81/16.94 (![State: $i] : holds(clear(table), State) <=> ![State: $i] : holds(clear(table), State)),
% 25.81/16.94 inference(quant_intro,[status(thm)],[117])).
% 25.81/16.94 tff(119,plain,
% 25.81/16.94 (![State: $i] : holds(clear(table), State) <=> ![State: $i] : holds(clear(table), State)),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(120,axiom,(![State: $i] : holds(clear(table), State)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','clear_table')).
% 25.81/16.94 tff(121,plain,
% 25.81/16.94 (![State: $i] : holds(clear(table), State)),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[120, 119])).
% 25.81/16.94 tff(122,plain,(
% 25.81/16.94 ![State: $i] : holds(clear(table), State)),
% 25.81/16.94 inference(skolemize,[status(sab)],[121])).
% 25.81/16.94 tff(123,plain,
% 25.81/16.94 (![State: $i] : holds(clear(table), State)),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[122, 118])).
% 25.81/16.94 tff(124,plain,
% 25.81/16.94 ((~![State: $i] : holds(clear(table), State)) | holds(clear(table), s0)),
% 25.81/16.94 inference(quant_inst,[status(thm)],[])).
% 25.81/16.94 tff(125,plain,
% 25.81/16.94 (holds(clear(table), s0)),
% 25.81/16.94 inference(unit_resolution,[status(thm)],[124, 123])).
% 25.81/16.94 tff(126,plain,
% 25.81/16.94 (differ(c, table) <=> differ(c, table)),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(127,axiom,(differ(c, table)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','differ_c_table')).
% 25.81/16.94 tff(128,plain,
% 25.81/16.94 (differ(c, table)),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[127, 126])).
% 25.81/16.94 tff(129,plain,
% 25.81/16.94 (((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | ((~differ(c, table)) | differ(table, c))) <=> ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | (~differ(c, table)) | differ(table, c))),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(130,plain,
% 25.81/16.94 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | ((~differ(c, table)) | differ(table, c))),
% 25.81/16.94 inference(quant_inst,[status(thm)],[])).
% 25.81/16.94 tff(131,plain,
% 25.81/16.94 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | (~differ(c, table)) | differ(table, c)),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[130, 129])).
% 25.81/16.94 tff(132,plain,
% 25.81/16.94 (differ(table, c)),
% 25.81/16.94 inference(unit_resolution,[status(thm)],[131, 59, 128])).
% 25.81/16.94 tff(133,plain,
% 25.81/16.94 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (holds(clear(table), do(pickup(c), s0)) | (~holds(clear(table), s0)) | (~differ(table, c)))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | holds(clear(table), do(pickup(c), s0)) | (~holds(clear(table), s0)) | (~differ(table, c)))),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(134,plain,
% 25.81/16.94 (((~holds(clear(table), s0)) | (~differ(table, c)) | holds(clear(table), do(pickup(c), s0))) <=> (holds(clear(table), do(pickup(c), s0)) | (~holds(clear(table), s0)) | (~differ(table, c)))),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(135,plain,
% 25.81/16.94 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(table), s0)) | (~differ(table, c)) | holds(clear(table), do(pickup(c), s0)))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (holds(clear(table), do(pickup(c), s0)) | (~holds(clear(table), s0)) | (~differ(table, c))))),
% 25.81/16.94 inference(monotonicity,[status(thm)],[134])).
% 25.81/16.94 tff(136,plain,
% 25.81/16.94 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(table), s0)) | (~differ(table, c)) | holds(clear(table), do(pickup(c), s0)))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | holds(clear(table), do(pickup(c), s0)) | (~holds(clear(table), s0)) | (~differ(table, c)))),
% 25.81/16.94 inference(transitivity,[status(thm)],[135, 133])).
% 25.81/16.94 tff(137,plain,
% 25.81/16.94 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(table), s0)) | (~differ(table, c)) | holds(clear(table), do(pickup(c), s0)))),
% 25.81/16.94 inference(quant_inst,[status(thm)],[])).
% 25.81/16.94 tff(138,plain,
% 25.81/16.94 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | holds(clear(table), do(pickup(c), s0)) | (~holds(clear(table), s0)) | (~differ(table, c))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[137, 136])).
% 25.81/16.94 tff(139,plain,
% 25.81/16.94 ($false),
% 25.81/16.94 inference(unit_resolution,[status(thm)],[138, 73, 132, 125, 116])).
% 25.81/16.94 tff(140,plain,(holds(clear(table), do(pickup(c), s0))), inference(lemma,lemma(discharge,[]))).
% 25.81/16.94 tff(141,plain,
% 25.81/16.94 (^[State: $i, X: $i] : refl(((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State))) <=> ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State))))),
% 25.81/16.94 inference(bind,[status(th)],[])).
% 25.81/16.94 tff(142,plain,
% 25.81/16.94 (![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State))) <=> ![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 25.81/16.94 inference(quant_intro,[status(thm)],[141])).
% 25.81/16.94 tff(143,plain,
% 25.81/16.94 (![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State))) <=> ![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(144,plain,
% 25.81/16.94 (^[State: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((holds(holding(X), do(pickup(X), State)) | (~holds(empty, State))) <=> ((~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))), (((holds(holding(X), do(pickup(X), State)) | (~holds(empty, State))) | (~holds(clear(X), State))) <=> (((~holds(empty, State)) | holds(holding(X), do(pickup(X), State))) | (~holds(clear(X), State))))), rewrite((((~holds(empty, State)) | holds(holding(X), do(pickup(X), State))) | (~holds(clear(X), State))) <=> ((~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))), (((holds(holding(X), do(pickup(X), State)) | (~holds(empty, State))) | (~holds(clear(X), State))) <=> ((~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State))))), ((((holds(holding(X), do(pickup(X), State)) | (~holds(empty, State))) | (~holds(clear(X), State))) | (~differ(X, table))) <=> (((~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State))) | (~differ(X, table))))), rewrite((((~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State))) | (~differ(X, table))) <=> ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))), ((((holds(holding(X), do(pickup(X), State)) | (~holds(empty, State))) | (~holds(clear(X), State))) | (~differ(X, table))) <=> ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))))),
% 25.81/16.94 inference(bind,[status(th)],[])).
% 25.81/16.94 tff(145,plain,
% 25.81/16.94 (![State: $i, X: $i] : (((holds(holding(X), do(pickup(X), State)) | (~holds(empty, State))) | (~holds(clear(X), State))) | (~differ(X, table))) <=> ![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 25.81/16.94 inference(quant_intro,[status(thm)],[144])).
% 25.81/16.94 tff(146,axiom,(![State: $i, X: $i] : (((holds(holding(X), do(pickup(X), State)) | (~holds(empty, State))) | (~holds(clear(X), State))) | (~differ(X, table)))), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-0.ax','pickup_1')).
% 25.81/16.94 tff(147,plain,
% 25.81/16.94 (![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[146, 145])).
% 25.81/16.94 tff(148,plain,
% 25.81/16.94 (![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[147, 143])).
% 25.81/16.94 tff(149,plain,(
% 25.81/16.94 ![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 25.81/16.94 inference(skolemize,[status(sab)],[148])).
% 25.81/16.94 tff(150,plain,
% 25.81/16.94 (![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[149, 142])).
% 25.81/16.94 tff(151,plain,
% 25.81/16.94 (((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | ((~holds(empty, s0)) | (~holds(clear(c), s0)) | (~differ(c, table)) | holds(holding(c), do(pickup(c), s0)))) <=> ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | (~holds(empty, s0)) | (~holds(clear(c), s0)) | (~differ(c, table)) | holds(holding(c), do(pickup(c), s0)))),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(152,plain,
% 25.81/16.94 (((~differ(c, table)) | (~holds(clear(c), s0)) | (~holds(empty, s0)) | holds(holding(c), do(pickup(c), s0))) <=> ((~holds(empty, s0)) | (~holds(clear(c), s0)) | (~differ(c, table)) | holds(holding(c), do(pickup(c), s0)))),
% 25.81/16.94 inference(rewrite,[status(thm)],[])).
% 25.81/16.94 tff(153,plain,
% 25.81/16.94 (((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | ((~differ(c, table)) | (~holds(clear(c), s0)) | (~holds(empty, s0)) | holds(holding(c), do(pickup(c), s0)))) <=> ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | ((~holds(empty, s0)) | (~holds(clear(c), s0)) | (~differ(c, table)) | holds(holding(c), do(pickup(c), s0))))),
% 25.81/16.94 inference(monotonicity,[status(thm)],[152])).
% 25.81/16.94 tff(154,plain,
% 25.81/16.94 (((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | ((~differ(c, table)) | (~holds(clear(c), s0)) | (~holds(empty, s0)) | holds(holding(c), do(pickup(c), s0)))) <=> ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | (~holds(empty, s0)) | (~holds(clear(c), s0)) | (~differ(c, table)) | holds(holding(c), do(pickup(c), s0)))),
% 25.81/16.94 inference(transitivity,[status(thm)],[153, 151])).
% 25.81/16.94 tff(155,plain,
% 25.81/16.94 ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | ((~differ(c, table)) | (~holds(clear(c), s0)) | (~holds(empty, s0)) | holds(holding(c), do(pickup(c), s0)))),
% 25.81/16.94 inference(quant_inst,[status(thm)],[])).
% 25.81/16.94 tff(156,plain,
% 25.81/16.94 ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | (~holds(empty, s0)) | (~holds(clear(c), s0)) | (~differ(c, table)) | holds(holding(c), do(pickup(c), s0))),
% 25.81/16.94 inference(modus_ponens,[status(thm)],[155, 154])).
% 25.81/16.94 tff(157,plain,
% 25.81/16.94 (holds(holding(c), do(pickup(c), s0))),
% 25.81/16.94 inference(unit_resolution,[status(thm)],[156, 150, 128, 8, 5])).
% 25.81/16.94 tff(158,plain,
% 25.81/16.94 (^[Y: $i, State: $i, X: $i] : refl(((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State))) <=> ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State))))),
% 25.81/16.94 inference(bind,[status(th)],[])).
% 25.81/16.94 tff(159,plain,
% 25.81/16.94 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State))) <=> ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 25.81/16.95 inference(quant_intro,[status(thm)],[158])).
% 25.81/16.95 tff(160,plain,
% 25.81/16.95 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State))) <=> ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 25.81/16.95 inference(rewrite,[status(thm)],[])).
% 25.81/16.95 tff(161,plain,
% 25.81/16.95 (^[Y: $i, State: $i, X: $i] : trans(monotonicity(rewrite((holds(empty, do(putdown(X, Y), State)) | (~holds(holding(X), State))) <=> ((~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))), (((holds(empty, do(putdown(X, Y), State)) | (~holds(holding(X), State))) | (~holds(clear(Y), State))) <=> (((~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State))) | (~holds(clear(Y), State))))), rewrite((((~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State))) | (~holds(clear(Y), State))) <=> ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))), (((holds(empty, do(putdown(X, Y), State)) | (~holds(holding(X), State))) | (~holds(clear(Y), State))) <=> ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))))),
% 25.81/16.95 inference(bind,[status(th)],[])).
% 25.81/16.95 tff(162,plain,
% 25.81/16.95 (![Y: $i, State: $i, X: $i] : ((holds(empty, do(putdown(X, Y), State)) | (~holds(holding(X), State))) | (~holds(clear(Y), State))) <=> ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 25.81/16.95 inference(quant_intro,[status(thm)],[161])).
% 25.81/16.95 tff(163,axiom,(![Y: $i, State: $i, X: $i] : ((holds(empty, do(putdown(X, Y), State)) | (~holds(holding(X), State))) | (~holds(clear(Y), State)))), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-0.ax','putdown_1')).
% 25.81/16.95 tff(164,plain,
% 25.81/16.95 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 25.81/16.95 inference(modus_ponens,[status(thm)],[163, 162])).
% 25.81/16.95 tff(165,plain,
% 25.81/16.95 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 25.81/16.95 inference(modus_ponens,[status(thm)],[164, 160])).
% 25.81/16.95 tff(166,plain,(
% 25.81/16.95 ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 25.81/16.95 inference(skolemize,[status(sab)],[165])).
% 25.81/16.95 tff(167,plain,
% 25.81/16.95 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 25.81/16.95 inference(modus_ponens,[status(thm)],[166, 159])).
% 25.81/16.95 tff(168,plain,
% 25.81/16.95 (((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | ((~holds(clear(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(empty, do(putdown(c, table), do(pickup(c), s0))))) <=> ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | (~holds(clear(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(empty, do(putdown(c, table), do(pickup(c), s0))))),
% 25.81/16.95 inference(rewrite,[status(thm)],[])).
% 25.81/16.95 tff(169,plain,
% 25.81/16.95 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | ((~holds(clear(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(empty, do(putdown(c, table), do(pickup(c), s0))))),
% 25.81/16.95 inference(quant_inst,[status(thm)],[])).
% 25.81/16.95 tff(170,plain,
% 25.81/16.95 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | (~holds(clear(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(empty, do(putdown(c, table), do(pickup(c), s0)))),
% 25.83/16.95 inference(modus_ponens,[status(thm)],[169, 168])).
% 25.83/16.95 tff(171,plain,
% 25.83/16.95 (holds(empty, do(putdown(c, table), do(pickup(c), s0)))),
% 25.83/16.95 inference(unit_resolution,[status(thm)],[170, 167, 157, 140])).
% 25.83/16.95 tff(172,plain,
% 25.83/16.95 (((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | ((~differ(a, table)) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | (~holds(clear(a), do(putdown(c, table), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) <=> ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | (~differ(a, table)) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | (~holds(clear(a), do(putdown(c, table), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))),
% 25.83/16.95 inference(rewrite,[status(thm)],[])).
% 25.83/16.95 tff(173,plain,
% 25.83/16.95 (((~differ(a, table)) | (~holds(clear(a), do(putdown(c, table), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) <=> ((~differ(a, table)) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | (~holds(clear(a), do(putdown(c, table), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))),
% 25.83/16.95 inference(rewrite,[status(thm)],[])).
% 25.83/16.95 tff(174,plain,
% 25.83/16.95 (((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | ((~differ(a, table)) | (~holds(clear(a), do(putdown(c, table), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) <=> ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | ((~differ(a, table)) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | (~holds(clear(a), do(putdown(c, table), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))),
% 25.83/16.95 inference(monotonicity,[status(thm)],[173])).
% 25.83/16.95 tff(175,plain,
% 25.83/16.95 (((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | ((~differ(a, table)) | (~holds(clear(a), do(putdown(c, table), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) <=> ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | (~differ(a, table)) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | (~holds(clear(a), do(putdown(c, table), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))),
% 25.83/16.95 inference(transitivity,[status(thm)],[174, 172])).
% 25.83/16.95 tff(176,plain,
% 25.83/16.95 ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | ((~differ(a, table)) | (~holds(clear(a), do(putdown(c, table), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))),
% 25.83/16.95 inference(quant_inst,[status(thm)],[])).
% 25.83/16.95 tff(177,plain,
% 25.83/16.95 ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | (~differ(a, table)) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | (~holds(clear(a), do(putdown(c, table), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))),
% 25.83/16.95 inference(modus_ponens,[status(thm)],[176, 175])).
% 25.83/16.95 tff(178,plain,
% 25.83/16.95 ((~holds(clear(a), do(putdown(c, table), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))),
% 25.83/16.95 inference(unit_resolution,[status(thm)],[177, 150, 110, 171])).
% 25.83/16.95 tff(179,plain,
% 25.83/16.95 (holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))),
% 25.83/16.95 inference(unit_resolution,[status(thm)],[178, 115])).
% 25.83/16.95 tff(180,assumption,(~holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))), introduced(assumption)).
% 25.83/16.95 tff(181,plain,
% 25.83/16.95 (^[Y: $i, State: $i, X: $i] : refl(((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State))) <=> ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State))))),
% 25.83/16.95 inference(bind,[status(th)],[])).
% 25.83/16.95 tff(182,plain,
% 25.83/16.95 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State))) <=> ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 25.83/16.95 inference(quant_intro,[status(thm)],[181])).
% 25.83/16.95 tff(183,plain,
% 25.83/16.95 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State))) <=> ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 25.83/16.95 inference(rewrite,[status(thm)],[])).
% 25.83/16.95 tff(184,plain,
% 25.83/16.95 (^[Y: $i, State: $i, X: $i] : trans(monotonicity(rewrite((holds(clear(X), do(putdown(X, Y), State)) | (~holds(holding(X), State))) <=> ((~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))), (((holds(clear(X), do(putdown(X, Y), State)) | (~holds(holding(X), State))) | (~holds(clear(Y), State))) <=> (((~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State))) | (~holds(clear(Y), State))))), rewrite((((~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State))) | (~holds(clear(Y), State))) <=> ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))), (((holds(clear(X), do(putdown(X, Y), State)) | (~holds(holding(X), State))) | (~holds(clear(Y), State))) <=> ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))))),
% 25.83/16.95 inference(bind,[status(th)],[])).
% 25.83/16.95 tff(185,plain,
% 25.83/16.95 (![Y: $i, State: $i, X: $i] : ((holds(clear(X), do(putdown(X, Y), State)) | (~holds(holding(X), State))) | (~holds(clear(Y), State))) <=> ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 25.83/16.95 inference(quant_intro,[status(thm)],[184])).
% 25.83/16.95 tff(186,axiom,(![Y: $i, State: $i, X: $i] : ((holds(clear(X), do(putdown(X, Y), State)) | (~holds(holding(X), State))) | (~holds(clear(Y), State)))), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-0.ax','putdown_3')).
% 25.83/16.95 tff(187,plain,
% 25.83/16.95 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 25.83/16.95 inference(modus_ponens,[status(thm)],[186, 185])).
% 25.83/16.95 tff(188,plain,
% 25.83/16.95 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 25.83/16.95 inference(modus_ponens,[status(thm)],[187, 183])).
% 25.83/16.95 tff(189,plain,(
% 25.83/16.95 ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 25.83/16.95 inference(skolemize,[status(sab)],[188])).
% 25.83/16.95 tff(190,plain,
% 25.83/16.95 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 25.83/16.95 inference(modus_ponens,[status(thm)],[189, 182])).
% 25.83/16.95 tff(191,plain,
% 25.83/16.95 (((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | ((~holds(clear(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(clear(c), do(putdown(c, table), do(pickup(c), s0))))) <=> ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | (~holds(clear(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(clear(c), do(putdown(c, table), do(pickup(c), s0))))),
% 25.83/16.95 inference(rewrite,[status(thm)],[])).
% 25.83/16.95 tff(192,plain,
% 25.83/16.95 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | ((~holds(clear(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(clear(c), do(putdown(c, table), do(pickup(c), s0))))),
% 25.83/16.95 inference(quant_inst,[status(thm)],[])).
% 25.83/16.95 tff(193,plain,
% 25.83/16.95 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | (~holds(clear(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(clear(c), do(putdown(c, table), do(pickup(c), s0)))),
% 25.83/16.95 inference(modus_ponens,[status(thm)],[192, 191])).
% 25.83/16.95 tff(194,plain,
% 25.83/16.95 (holds(clear(c), do(putdown(c, table), do(pickup(c), s0)))),
% 25.83/16.95 inference(unit_resolution,[status(thm)],[193, 190, 157, 140])).
% 25.83/16.95 tff(195,plain,
% 25.83/16.95 (((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | ((~differ(a, c)) | differ(c, a))) <=> ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | (~differ(a, c)) | differ(c, a))),
% 25.83/16.95 inference(rewrite,[status(thm)],[])).
% 25.83/16.95 tff(196,plain,
% 25.83/16.95 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | ((~differ(a, c)) | differ(c, a))),
% 25.83/16.95 inference(quant_inst,[status(thm)],[])).
% 25.83/16.95 tff(197,plain,
% 25.83/16.95 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | (~differ(a, c)) | differ(c, a)),
% 25.83/16.95 inference(modus_ponens,[status(thm)],[196, 195])).
% 25.83/16.95 tff(198,plain,
% 25.83/16.95 (differ(c, a)),
% 25.83/16.95 inference(unit_resolution,[status(thm)],[197, 59, 102])).
% 25.83/16.95 tff(199,plain,
% 25.83/16.95 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(c), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(c, a)))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~holds(clear(c), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(c, a)))),
% 25.83/16.95 inference(rewrite,[status(thm)],[])).
% 25.83/16.95 tff(200,plain,
% 25.83/16.95 (((~holds(clear(c), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(c, a)) | holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) <=> ((~holds(clear(c), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(c, a)))),
% 25.83/16.95 inference(rewrite,[status(thm)],[])).
% 25.83/16.95 tff(201,plain,
% 25.83/16.95 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(c), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(c, a)) | holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(c), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(c, a))))),
% 25.83/16.95 inference(monotonicity,[status(thm)],[200])).
% 25.83/16.95 tff(202,plain,
% 25.83/16.95 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(c), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(c, a)) | holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~holds(clear(c), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(c, a)))),
% 25.83/16.95 inference(transitivity,[status(thm)],[201, 199])).
% 25.83/16.95 tff(203,plain,
% 25.83/16.95 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(c), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(c, a)) | holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))),
% 25.83/16.95 inference(quant_inst,[status(thm)],[])).
% 25.83/16.95 tff(204,plain,
% 25.83/16.95 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~holds(clear(c), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(c, a))),
% 25.83/16.95 inference(modus_ponens,[status(thm)],[203, 202])).
% 25.83/16.95 tff(205,plain,
% 25.83/16.95 ($false),
% 25.83/16.95 inference(unit_resolution,[status(thm)],[204, 73, 198, 194, 180])).
% 25.83/16.95 tff(206,plain,(holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))), inference(lemma,lemma(discharge,[]))).
% 25.83/16.95 tff(207,plain,
% 25.83/16.95 (((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | ((~holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | (~holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | holds(empty, do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))) <=> ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | (~holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | (~holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | holds(empty, do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))),
% 25.83/16.95 inference(rewrite,[status(thm)],[])).
% 25.83/16.95 tff(208,plain,
% 25.83/16.95 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | ((~holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | (~holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | holds(empty, do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))),
% 25.83/16.95 inference(quant_inst,[status(thm)],[])).
% 25.83/16.95 tff(209,plain,
% 25.83/16.95 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | (~holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | (~holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | holds(empty, do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))),
% 25.83/16.95 inference(modus_ponens,[status(thm)],[208, 207])).
% 25.83/16.95 tff(210,plain,
% 25.83/16.95 (holds(empty, do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))),
% 25.83/16.95 inference(unit_resolution,[status(thm)],[209, 167, 206, 179])).
% 25.83/16.95 tff(211,plain,
% 25.83/16.95 (((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | ((~differ(d, table)) | (~holds(empty, do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | holds(holding(d), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(clear(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))))) <=> ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | (~differ(d, table)) | (~holds(empty, do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | holds(holding(d), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(clear(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))))),
% 25.83/16.95 inference(rewrite,[status(thm)],[])).
% 25.83/16.95 tff(212,plain,
% 25.83/16.95 (((~differ(d, table)) | (~holds(clear(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(empty, do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | holds(holding(d), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))) <=> ((~differ(d, table)) | (~holds(empty, do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | holds(holding(d), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(clear(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))))),
% 25.83/16.95 inference(rewrite,[status(thm)],[])).
% 25.83/16.95 tff(213,plain,
% 25.83/16.95 (((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | ((~differ(d, table)) | (~holds(clear(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(empty, do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | holds(holding(d), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))))) <=> ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | ((~differ(d, table)) | (~holds(empty, do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | holds(holding(d), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(clear(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))))),
% 25.83/16.95 inference(monotonicity,[status(thm)],[212])).
% 25.83/16.95 tff(214,plain,
% 25.83/16.95 (((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | ((~differ(d, table)) | (~holds(clear(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(empty, do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | holds(holding(d), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))))) <=> ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | (~differ(d, table)) | (~holds(empty, do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | holds(holding(d), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(clear(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))))),
% 25.83/16.95 inference(transitivity,[status(thm)],[213, 211])).
% 25.83/16.95 tff(215,plain,
% 25.83/16.95 ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | ((~differ(d, table)) | (~holds(clear(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(empty, do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | holds(holding(d), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))))),
% 25.83/16.95 inference(quant_inst,[status(thm)],[])).
% 25.83/16.95 tff(216,plain,
% 25.83/16.95 ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | (~differ(d, table)) | (~holds(empty, do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | holds(holding(d), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(clear(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))),
% 25.83/16.95 inference(modus_ponens,[status(thm)],[215, 214])).
% 25.83/16.95 tff(217,plain,
% 25.83/16.95 (holds(holding(d), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(clear(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))),
% 25.83/16.95 inference(unit_resolution,[status(thm)],[216, 150, 31, 210])).
% 25.83/16.95 tff(218,plain,
% 25.83/16.95 (holds(holding(d), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))),
% 25.83/16.95 inference(unit_resolution,[status(thm)],[217, 94])).
% 25.83/16.95 tff(219,assumption,(~holds(clear(a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))), introduced(assumption)).
% 25.83/16.96 tff(220,plain,
% 25.83/16.96 (((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | ((~holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | (~holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | holds(clear(a), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))) <=> ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | (~holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | (~holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | holds(clear(a), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))),
% 25.83/16.96 inference(rewrite,[status(thm)],[])).
% 25.83/16.96 tff(221,plain,
% 25.83/16.96 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | ((~holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | (~holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | holds(clear(a), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))),
% 25.83/16.96 inference(quant_inst,[status(thm)],[])).
% 25.83/16.96 tff(222,plain,
% 25.83/16.96 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | (~holds(clear(c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | (~holds(holding(a), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))) | holds(clear(a), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))),
% 25.83/16.96 inference(modus_ponens,[status(thm)],[221, 220])).
% 25.83/16.96 tff(223,plain,
% 25.83/16.96 (holds(clear(a), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))),
% 25.83/16.96 inference(unit_resolution,[status(thm)],[222, 190, 206, 179])).
% 25.83/16.96 tff(224,plain,
% 25.83/16.96 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~differ(a, d)) | (~holds(clear(a), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | holds(clear(a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~differ(a, d)) | (~holds(clear(a), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | holds(clear(a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))))),
% 25.83/16.96 inference(rewrite,[status(thm)],[])).
% 25.83/16.96 tff(225,plain,
% 25.83/16.96 (((~holds(clear(a), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | (~differ(a, d)) | holds(clear(a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))) <=> ((~differ(a, d)) | (~holds(clear(a), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | holds(clear(a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))))),
% 25.83/16.96 inference(rewrite,[status(thm)],[])).
% 25.83/16.96 tff(226,plain,
% 25.83/16.96 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(a), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | (~differ(a, d)) | holds(clear(a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~differ(a, d)) | (~holds(clear(a), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | holds(clear(a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))))),
% 25.83/16.96 inference(monotonicity,[status(thm)],[225])).
% 25.83/16.96 tff(227,plain,
% 25.83/16.96 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(a), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | (~differ(a, d)) | holds(clear(a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~differ(a, d)) | (~holds(clear(a), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | holds(clear(a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))))),
% 25.83/16.96 inference(transitivity,[status(thm)],[226, 224])).
% 25.83/16.96 tff(228,plain,
% 25.83/16.96 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(a), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | (~differ(a, d)) | holds(clear(a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))))),
% 25.83/16.96 inference(quant_inst,[status(thm)],[])).
% 25.83/16.96 tff(229,plain,
% 25.83/16.96 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~differ(a, d)) | (~holds(clear(a), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))) | holds(clear(a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))),
% 25.83/16.96 inference(modus_ponens,[status(thm)],[228, 227])).
% 25.83/16.96 tff(230,plain,
% 25.83/16.96 ($false),
% 25.83/16.96 inference(unit_resolution,[status(thm)],[229, 73, 49, 223, 219])).
% 25.83/16.96 tff(231,plain,(holds(clear(a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))), inference(lemma,lemma(discharge,[]))).
% 25.83/16.96 tff(232,plain,
% 25.83/16.96 (^[Y: $i, State: $i, X: $i] : refl(((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State))) <=> ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State))))),
% 25.83/16.96 inference(bind,[status(th)],[])).
% 25.83/16.96 tff(233,plain,
% 25.83/16.96 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State))) <=> ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 25.83/16.96 inference(quant_intro,[status(thm)],[232])).
% 25.83/16.96 tff(234,plain,
% 25.83/16.96 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State))) <=> ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 25.83/16.96 inference(rewrite,[status(thm)],[])).
% 25.83/16.96 tff(235,plain,
% 25.83/16.96 (^[Y: $i, State: $i, X: $i] : trans(monotonicity(rewrite((holds(on(X, Y), do(putdown(X, Y), State)) | (~holds(holding(X), State))) <=> ((~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))), (((holds(on(X, Y), do(putdown(X, Y), State)) | (~holds(holding(X), State))) | (~holds(clear(Y), State))) <=> (((~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State))) | (~holds(clear(Y), State))))), rewrite((((~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State))) | (~holds(clear(Y), State))) <=> ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))), (((holds(on(X, Y), do(putdown(X, Y), State)) | (~holds(holding(X), State))) | (~holds(clear(Y), State))) <=> ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))))),
% 25.83/16.96 inference(bind,[status(th)],[])).
% 25.83/16.96 tff(236,plain,
% 25.83/16.96 (![Y: $i, State: $i, X: $i] : ((holds(on(X, Y), do(putdown(X, Y), State)) | (~holds(holding(X), State))) | (~holds(clear(Y), State))) <=> ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 25.83/16.96 inference(quant_intro,[status(thm)],[235])).
% 25.83/16.96 tff(237,axiom,(![Y: $i, State: $i, X: $i] : ((holds(on(X, Y), do(putdown(X, Y), State)) | (~holds(holding(X), State))) | (~holds(clear(Y), State)))), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-0.ax','putdown_2')).
% 25.83/16.96 tff(238,plain,
% 25.83/16.96 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 25.83/16.96 inference(modus_ponens,[status(thm)],[237, 236])).
% 25.83/16.96 tff(239,plain,
% 25.83/16.96 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 25.83/16.96 inference(modus_ponens,[status(thm)],[238, 234])).
% 25.83/16.96 tff(240,plain,(
% 25.83/16.96 ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 25.83/16.96 inference(skolemize,[status(sab)],[239])).
% 25.83/16.96 tff(241,plain,
% 25.83/16.96 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 25.83/16.96 inference(modus_ponens,[status(thm)],[240, 233])).
% 25.83/16.96 tff(242,plain,
% 25.83/16.96 (((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))) | ((~holds(clear(a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))) | (~holds(holding(d), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))) | holds(on(d, a), do(putdown(d, a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))))) <=> ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))) | (~holds(clear(a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))) | (~holds(holding(d), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))) | holds(on(d, a), do(putdown(d, a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))))),
% 25.83/16.96 inference(rewrite,[status(thm)],[])).
% 25.83/16.96 tff(243,plain,
% 25.83/16.96 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))) | ((~holds(clear(a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))) | (~holds(holding(d), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))) | holds(on(d, a), do(putdown(d, a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))))),
% 25.83/16.96 inference(quant_inst,[status(thm)],[])).
% 25.83/16.96 tff(244,plain,
% 25.83/16.96 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))) | (~holds(clear(a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))) | (~holds(holding(d), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))) | holds(on(d, a), do(putdown(d, a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))))),
% 25.83/16.96 inference(modus_ponens,[status(thm)],[243, 242])).
% 25.83/16.96 tff(245,plain,
% 25.83/16.96 (holds(on(d, a), do(putdown(d, a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0)))))))),
% 25.83/16.96 inference(unit_resolution,[status(thm)],[244, 241, 231, 218])).
% 25.83/16.96 tff(246,plain,
% 25.83/16.96 (^[State: $i] : refl((~holds(on(d, a), State)) <=> (~holds(on(d, a), State)))),
% 25.83/16.96 inference(bind,[status(th)],[])).
% 25.83/16.96 tff(247,plain,
% 25.83/16.96 (![State: $i] : (~holds(on(d, a), State)) <=> ![State: $i] : (~holds(on(d, a), State))),
% 25.83/16.96 inference(quant_intro,[status(thm)],[246])).
% 25.83/16.96 tff(248,plain,
% 25.83/16.96 (![State: $i] : (~holds(on(d, a), State)) <=> ![State: $i] : (~holds(on(d, a), State))),
% 25.83/16.96 inference(rewrite,[status(thm)],[])).
% 25.83/16.96 tff(249,axiom,(![State: $i] : (~holds(on(d, a), State))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_DA')).
% 25.83/16.96 tff(250,plain,
% 25.83/16.96 (![State: $i] : (~holds(on(d, a), State))),
% 25.83/16.96 inference(modus_ponens,[status(thm)],[249, 248])).
% 25.83/16.96 tff(251,plain,(
% 25.83/16.96 ![State: $i] : (~holds(on(d, a), State))),
% 25.83/16.96 inference(skolemize,[status(sab)],[250])).
% 25.83/16.96 tff(252,plain,
% 25.83/16.96 (![State: $i] : (~holds(on(d, a), State))),
% 25.83/16.96 inference(modus_ponens,[status(thm)],[251, 247])).
% 25.83/16.96 tff(253,plain,
% 25.83/16.96 ((~![State: $i] : (~holds(on(d, a), State))) | (~holds(on(d, a), do(putdown(d, a), do(pickup(d), do(putdown(a, c), do(pickup(a), do(putdown(c, table), do(pickup(c), s0))))))))),
% 25.83/16.96 inference(quant_inst,[status(thm)],[])).
% 25.83/16.96 tff(254,plain,
% 25.83/16.96 ($false),
% 25.83/16.96 inference(unit_resolution,[status(thm)],[253, 252, 245])).
% 25.83/16.96 % SZS output end Proof
%------------------------------------------------------------------------------