TSTP Solution File: PLA017-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PLA017-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 2.10s 1.59s
% Output : Proof 2.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : PLA017-1 : TPTP v8.1.0. Released v1.1.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n015.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Sep 2 17:26:09 EDT 2022
% 0.12/0.32 % 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.
% 2.10/1.59 % SZS status Unsatisfiable
% 2.10/1.59 % SZS output start Proof
% 2.10/1.59 tff(holds_type, type, (
% 2.10/1.59 holds: ( $i * $i ) > $o)).
% 2.10/1.59 tff(do_type, type, (
% 2.10/1.59 do: ( $i * $i ) > $i)).
% 2.10/1.59 tff(s0_type, type, (
% 2.10/1.59 s0: $i)).
% 2.10/1.59 tff(pickup_type, type, (
% 2.10/1.59 pickup: $i > $i)).
% 2.10/1.59 tff(c_type, type, (
% 2.10/1.59 c: $i)).
% 2.10/1.59 tff(putdown_type, type, (
% 2.10/1.59 putdown: ( $i * $i ) > $i)).
% 2.10/1.59 tff(d_type, type, (
% 2.10/1.59 d: $i)).
% 2.10/1.59 tff(a_type, type, (
% 2.10/1.59 a: $i)).
% 2.10/1.59 tff(on_type, type, (
% 2.10/1.59 on: ( $i * $i ) > $i)).
% 2.10/1.59 tff(clear_type, type, (
% 2.10/1.59 clear: $i > $i)).
% 2.10/1.59 tff(holding_type, type, (
% 2.10/1.59 holding: $i > $i)).
% 2.10/1.59 tff(empty_type, type, (
% 2.10/1.59 empty: $i)).
% 2.10/1.59 tff(differ_type, type, (
% 2.10/1.59 differ: ( $i * $i ) > $o)).
% 2.10/1.59 tff(table_type, type, (
% 2.10/1.59 table: $i)).
% 2.10/1.59 tff(1,plain,
% 2.10/1.59 (holds(empty, s0) <=> holds(empty, s0)),
% 2.10/1.59 inference(rewrite,[status(thm)],[])).
% 2.10/1.59 tff(2,axiom,(holds(empty, s0)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','initial_state8')).
% 2.10/1.59 tff(3,plain,
% 2.10/1.59 (holds(empty, s0)),
% 2.10/1.59 inference(modus_ponens,[status(thm)],[2, 1])).
% 2.10/1.59 tff(4,plain,
% 2.10/1.59 (holds(clear(c), s0) <=> holds(clear(c), s0)),
% 2.10/1.59 inference(rewrite,[status(thm)],[])).
% 2.10/1.59 tff(5,axiom,(holds(clear(c), s0)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','initial_state7')).
% 2.10/1.59 tff(6,plain,
% 2.10/1.59 (holds(clear(c), s0)),
% 2.10/1.59 inference(modus_ponens,[status(thm)],[5, 4])).
% 2.10/1.59 tff(7,plain,
% 2.10/1.59 (differ(c, table) <=> differ(c, table)),
% 2.10/1.59 inference(rewrite,[status(thm)],[])).
% 2.10/1.59 tff(8,axiom,(differ(c, table)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','differ_c_table')).
% 2.10/1.59 tff(9,plain,
% 2.10/1.59 (differ(c, table)),
% 2.10/1.59 inference(modus_ponens,[status(thm)],[8, 7])).
% 2.10/1.59 tff(10,plain,
% 2.10/1.59 (^[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))))),
% 2.10/1.59 inference(bind,[status(th)],[])).
% 2.10/1.59 tff(11,plain,
% 2.10/1.59 (![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)))),
% 2.10/1.59 inference(quant_intro,[status(thm)],[10])).
% 2.10/1.59 tff(12,plain,
% 2.10/1.59 (![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)))),
% 2.10/1.59 inference(rewrite,[status(thm)],[])).
% 2.10/1.59 tff(13,plain,
% 2.10/1.59 (^[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)))))),
% 2.10/1.60 inference(bind,[status(th)],[])).
% 2.10/1.60 tff(14,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(quant_intro,[status(thm)],[13])).
% 2.10/1.60 tff(15,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/sandbox2/benchmark/Axioms/PLA001-0.ax','pickup_1')).
% 2.10/1.60 tff(16,plain,
% 2.10/1.60 (![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[15, 14])).
% 2.10/1.60 tff(17,plain,
% 2.10/1.60 (![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[16, 12])).
% 2.10/1.60 tff(18,plain,(
% 2.10/1.60 ![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 2.10/1.60 inference(skolemize,[status(sab)],[17])).
% 2.10/1.60 tff(19,plain,
% 2.10/1.60 (![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[18, 11])).
% 2.10/1.60 tff(20,plain,
% 2.10/1.60 (((~![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)))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(21,plain,
% 2.10/1.60 (((~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)))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(22,plain,
% 2.10/1.60 (((~![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))))),
% 2.10/1.60 inference(monotonicity,[status(thm)],[21])).
% 2.10/1.60 tff(23,plain,
% 2.10/1.60 (((~![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)))),
% 2.10/1.60 inference(transitivity,[status(thm)],[22, 20])).
% 2.10/1.60 tff(24,plain,
% 2.10/1.60 ((~![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)))),
% 2.10/1.60 inference(quant_inst,[status(thm)],[])).
% 2.10/1.60 tff(25,plain,
% 2.10/1.60 ((~![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))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[24, 23])).
% 2.10/1.60 tff(26,plain,
% 2.10/1.60 (holds(holding(c), do(pickup(c), s0))),
% 2.10/1.60 inference(unit_resolution,[status(thm)],[25, 19, 9, 6, 3])).
% 2.10/1.60 tff(27,plain,
% 2.10/1.60 (holds(on(c, d), s0) <=> holds(on(c, d), s0)),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(28,axiom,(holds(on(c, d), s0)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','initial_state3')).
% 2.10/1.60 tff(29,plain,
% 2.10/1.60 (holds(on(c, d), s0)),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[28, 27])).
% 2.10/1.60 tff(30,plain,
% 2.10/1.60 (^[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))))),
% 2.10/1.60 inference(bind,[status(th)],[])).
% 2.10/1.60 tff(31,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(quant_intro,[status(thm)],[30])).
% 2.10/1.60 tff(32,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(33,plain,
% 2.10/1.60 (^[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)))))),
% 2.10/1.60 inference(bind,[status(th)],[])).
% 2.10/1.60 tff(34,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(quant_intro,[status(thm)],[33])).
% 2.10/1.60 tff(35,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/sandbox2/benchmark/Axioms/PLA001-0.ax','pickup_2')).
% 2.10/1.60 tff(36,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[35, 34])).
% 2.10/1.60 tff(37,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[36, 32])).
% 2.10/1.60 tff(38,plain,(
% 2.10/1.60 ![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)))),
% 2.10/1.60 inference(skolemize,[status(sab)],[37])).
% 2.10/1.60 tff(39,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[38, 31])).
% 2.10/1.60 tff(40,plain,
% 2.10/1.60 (((~![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)))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(41,plain,
% 2.10/1.60 (((~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)))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(42,plain,
% 2.10/1.60 (((~![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))))),
% 2.10/1.60 inference(monotonicity,[status(thm)],[41])).
% 2.10/1.60 tff(43,plain,
% 2.10/1.60 (((~![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)))),
% 2.10/1.60 inference(transitivity,[status(thm)],[42, 40])).
% 2.10/1.60 tff(44,plain,
% 2.10/1.60 ((~![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)))),
% 2.10/1.60 inference(quant_inst,[status(thm)],[])).
% 2.10/1.60 tff(45,plain,
% 2.10/1.60 ((~![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))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[44, 43])).
% 2.10/1.60 tff(46,plain,
% 2.10/1.60 (holds(clear(d), do(pickup(c), s0))),
% 2.10/1.60 inference(unit_resolution,[status(thm)],[45, 39, 29, 6, 3])).
% 2.10/1.60 tff(47,plain,
% 2.10/1.60 (^[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))))),
% 2.10/1.60 inference(bind,[status(th)],[])).
% 2.10/1.60 tff(48,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(quant_intro,[status(thm)],[47])).
% 2.10/1.60 tff(49,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(50,plain,
% 2.10/1.60 (^[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)))))),
% 2.10/1.60 inference(bind,[status(th)],[])).
% 2.10/1.60 tff(51,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(quant_intro,[status(thm)],[50])).
% 2.10/1.60 tff(52,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/sandbox2/benchmark/Axioms/PLA001-0.ax','putdown_3')).
% 2.10/1.60 tff(53,plain,
% 2.10/1.60 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[52, 51])).
% 2.10/1.60 tff(54,plain,
% 2.10/1.60 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[53, 49])).
% 2.10/1.60 tff(55,plain,(
% 2.10/1.60 ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 2.10/1.60 inference(skolemize,[status(sab)],[54])).
% 2.10/1.60 tff(56,plain,
% 2.10/1.60 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[55, 48])).
% 2.10/1.60 tff(57,plain,
% 2.10/1.60 (((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | ((~holds(clear(d), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(clear(c), do(putdown(c, d), 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(d), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(clear(c), do(putdown(c, d), do(pickup(c), s0))))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(58,plain,
% 2.10/1.60 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | ((~holds(clear(d), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(clear(c), do(putdown(c, d), do(pickup(c), s0))))),
% 2.10/1.60 inference(quant_inst,[status(thm)],[])).
% 2.10/1.60 tff(59,plain,
% 2.10/1.60 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | (~holds(clear(d), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(clear(c), do(putdown(c, d), do(pickup(c), s0)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[58, 57])).
% 2.10/1.60 tff(60,plain,
% 2.10/1.60 (holds(clear(c), do(putdown(c, d), do(pickup(c), s0)))),
% 2.10/1.60 inference(unit_resolution,[status(thm)],[59, 56, 46, 26])).
% 2.10/1.60 tff(61,plain,
% 2.10/1.60 (differ(a, c) <=> differ(a, c)),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(62,axiom,(differ(a, c)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','differ_a_c')).
% 2.10/1.60 tff(63,plain,
% 2.10/1.60 (differ(a, c)),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[62, 61])).
% 2.10/1.60 tff(64,plain,
% 2.10/1.60 (^[Y: $i, X: $i] : refl(((~differ(Y, X)) | differ(X, Y)) <=> ((~differ(Y, X)) | differ(X, Y)))),
% 2.10/1.60 inference(bind,[status(th)],[])).
% 2.10/1.60 tff(65,plain,
% 2.10/1.60 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y)) <=> ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 2.10/1.60 inference(quant_intro,[status(thm)],[64])).
% 2.10/1.60 tff(66,plain,
% 2.10/1.60 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y)) <=> ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(67,plain,
% 2.10/1.60 (^[Y: $i, X: $i] : rewrite((differ(X, Y) | (~differ(Y, X))) <=> ((~differ(Y, X)) | differ(X, Y)))),
% 2.10/1.60 inference(bind,[status(th)],[])).
% 2.10/1.60 tff(68,plain,
% 2.10/1.60 (![Y: $i, X: $i] : (differ(X, Y) | (~differ(Y, X))) <=> ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 2.10/1.60 inference(quant_intro,[status(thm)],[67])).
% 2.10/1.60 tff(69,axiom,(![Y: $i, X: $i] : (differ(X, Y) | (~differ(Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','symmetry_of_differ')).
% 2.10/1.60 tff(70,plain,
% 2.10/1.60 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[69, 68])).
% 2.10/1.60 tff(71,plain,
% 2.10/1.60 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[70, 66])).
% 2.10/1.60 tff(72,plain,(
% 2.10/1.60 ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 2.10/1.60 inference(skolemize,[status(sab)],[71])).
% 2.10/1.60 tff(73,plain,
% 2.10/1.60 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[72, 65])).
% 2.10/1.60 tff(74,plain,
% 2.10/1.60 (((~![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))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(75,plain,
% 2.10/1.60 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | ((~differ(a, c)) | differ(c, a))),
% 2.10/1.60 inference(quant_inst,[status(thm)],[])).
% 2.10/1.60 tff(76,plain,
% 2.10/1.60 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | (~differ(a, c)) | differ(c, a)),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[75, 74])).
% 2.10/1.60 tff(77,plain,
% 2.10/1.60 (differ(c, a)),
% 2.10/1.60 inference(unit_resolution,[status(thm)],[76, 73, 63])).
% 2.10/1.60 tff(78,plain,
% 2.10/1.60 (^[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))))),
% 2.10/1.60 inference(bind,[status(th)],[])).
% 2.10/1.60 tff(79,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(quant_intro,[status(thm)],[78])).
% 2.10/1.60 tff(80,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(81,plain,
% 2.10/1.60 (^[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)))))),
% 2.10/1.60 inference(bind,[status(th)],[])).
% 2.10/1.60 tff(82,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(quant_intro,[status(thm)],[81])).
% 2.10/1.60 tff(83,axiom,(![Z: $i, State: $i, X: $i] : ((holds(clear(X), do(pickup(Z), State)) | (~holds(clear(X), State))) | (~differ(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-0.ax','pickup_4')).
% 2.10/1.60 tff(84,plain,
% 2.10/1.60 (![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[83, 82])).
% 2.10/1.60 tff(85,plain,
% 2.10/1.60 (![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[84, 80])).
% 2.10/1.60 tff(86,plain,(
% 2.10/1.60 ![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 2.10/1.60 inference(skolemize,[status(sab)],[85])).
% 2.10/1.60 tff(87,plain,
% 2.10/1.60 (![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[86, 79])).
% 2.10/1.60 tff(88,plain,
% 2.10/1.60 (((~![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, d), do(pickup(c), s0)))) | holds(clear(c), do(pickup(a), do(putdown(c, d), 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, d), do(pickup(c), s0)))) | holds(clear(c), do(pickup(a), do(putdown(c, d), do(pickup(c), s0)))) | (~differ(c, a)))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(89,plain,
% 2.10/1.60 (((~holds(clear(c), do(putdown(c, d), do(pickup(c), s0)))) | (~differ(c, a)) | holds(clear(c), do(pickup(a), do(putdown(c, d), do(pickup(c), s0))))) <=> ((~holds(clear(c), do(putdown(c, d), do(pickup(c), s0)))) | holds(clear(c), do(pickup(a), do(putdown(c, d), do(pickup(c), s0)))) | (~differ(c, a)))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(90,plain,
% 2.10/1.60 (((~![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, d), do(pickup(c), s0)))) | (~differ(c, a)) | holds(clear(c), do(pickup(a), do(putdown(c, d), 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, d), do(pickup(c), s0)))) | holds(clear(c), do(pickup(a), do(putdown(c, d), do(pickup(c), s0)))) | (~differ(c, a))))),
% 2.10/1.60 inference(monotonicity,[status(thm)],[89])).
% 2.10/1.60 tff(91,plain,
% 2.10/1.60 (((~![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, d), do(pickup(c), s0)))) | (~differ(c, a)) | holds(clear(c), do(pickup(a), do(putdown(c, d), 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, d), do(pickup(c), s0)))) | holds(clear(c), do(pickup(a), do(putdown(c, d), do(pickup(c), s0)))) | (~differ(c, a)))),
% 2.10/1.60 inference(transitivity,[status(thm)],[90, 88])).
% 2.10/1.60 tff(92,plain,
% 2.10/1.60 ((~![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, d), do(pickup(c), s0)))) | (~differ(c, a)) | holds(clear(c), do(pickup(a), do(putdown(c, d), do(pickup(c), s0)))))),
% 2.10/1.60 inference(quant_inst,[status(thm)],[])).
% 2.10/1.60 tff(93,plain,
% 2.10/1.60 ((~![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, d), do(pickup(c), s0)))) | holds(clear(c), do(pickup(a), do(putdown(c, d), do(pickup(c), s0)))) | (~differ(c, a))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[92, 91])).
% 2.10/1.60 tff(94,plain,
% 2.10/1.60 (holds(clear(c), do(pickup(a), do(putdown(c, d), do(pickup(c), s0))))),
% 2.10/1.60 inference(unit_resolution,[status(thm)],[93, 87, 77, 60])).
% 2.10/1.60 tff(95,assumption,(~holds(clear(a), do(putdown(c, d), do(pickup(c), s0)))), introduced(assumption)).
% 2.10/1.60 tff(96,assumption,(~holds(clear(a), do(pickup(c), s0))), introduced(assumption)).
% 2.10/1.60 tff(97,plain,
% 2.10/1.60 (holds(clear(a), s0) <=> holds(clear(a), s0)),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(98,axiom,(holds(clear(a), s0)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','initial_state5')).
% 2.10/1.60 tff(99,plain,
% 2.10/1.60 (holds(clear(a), s0)),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[98, 97])).
% 2.10/1.60 tff(100,plain,
% 2.10/1.60 (((~![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)))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(101,plain,
% 2.10/1.60 ((~![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)))),
% 2.10/1.60 inference(quant_inst,[status(thm)],[])).
% 2.10/1.60 tff(102,plain,
% 2.10/1.60 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~holds(clear(a), s0)) | (~differ(a, c)) | holds(clear(a), do(pickup(c), s0))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[101, 100])).
% 2.10/1.60 tff(103,plain,
% 2.10/1.60 ($false),
% 2.10/1.60 inference(unit_resolution,[status(thm)],[102, 87, 63, 99, 96])).
% 2.10/1.60 tff(104,plain,(holds(clear(a), do(pickup(c), s0))), inference(lemma,lemma(discharge,[]))).
% 2.10/1.60 tff(105,plain,
% 2.10/1.60 (differ(a, d) <=> differ(a, d)),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(106,axiom,(differ(a, d)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','differ_a_d')).
% 2.10/1.60 tff(107,plain,
% 2.10/1.60 (differ(a, d)),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[106, 105])).
% 2.10/1.60 tff(108,plain,
% 2.10/1.60 (^[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))))),
% 2.10/1.60 inference(bind,[status(th)],[])).
% 2.10/1.60 tff(109,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(quant_intro,[status(thm)],[108])).
% 2.10/1.60 tff(110,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(111,plain,
% 2.10/1.60 (^[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)))))),
% 2.10/1.60 inference(bind,[status(th)],[])).
% 2.10/1.60 tff(112,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(quant_intro,[status(thm)],[111])).
% 2.10/1.60 tff(113,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/sandbox2/benchmark/Axioms/PLA001-0.ax','putdown_5')).
% 2.10/1.60 tff(114,plain,
% 2.10/1.60 (![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[113, 112])).
% 2.10/1.60 tff(115,plain,
% 2.10/1.60 (![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[114, 110])).
% 2.10/1.60 tff(116,plain,(
% 2.10/1.60 ![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 2.10/1.60 inference(skolemize,[status(sab)],[115])).
% 2.10/1.60 tff(117,plain,
% 2.10/1.60 (![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[116, 109])).
% 2.10/1.60 tff(118,plain,
% 2.10/1.60 (((~![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, d)) | (~holds(clear(a), do(pickup(c), s0))) | holds(clear(a), do(putdown(c, d), 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, d)) | (~holds(clear(a), do(pickup(c), s0))) | holds(clear(a), do(putdown(c, d), do(pickup(c), s0))))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(119,plain,
% 2.10/1.60 ((~![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, d)) | (~holds(clear(a), do(pickup(c), s0))) | holds(clear(a), do(putdown(c, d), do(pickup(c), s0))))),
% 2.10/1.60 inference(quant_inst,[status(thm)],[])).
% 2.10/1.60 tff(120,plain,
% 2.10/1.60 ((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | (~differ(a, d)) | (~holds(clear(a), do(pickup(c), s0))) | holds(clear(a), do(putdown(c, d), do(pickup(c), s0)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[119, 118])).
% 2.10/1.60 tff(121,plain,
% 2.10/1.60 ($false),
% 2.10/1.60 inference(unit_resolution,[status(thm)],[120, 117, 107, 104, 95])).
% 2.10/1.60 tff(122,plain,(holds(clear(a), do(putdown(c, d), do(pickup(c), s0)))), inference(lemma,lemma(discharge,[]))).
% 2.10/1.60 tff(123,plain,
% 2.10/1.60 (^[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))))),
% 2.10/1.60 inference(bind,[status(th)],[])).
% 2.10/1.60 tff(124,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(quant_intro,[status(thm)],[123])).
% 2.10/1.60 tff(125,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(126,plain,
% 2.10/1.60 (^[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)))))),
% 2.10/1.60 inference(bind,[status(th)],[])).
% 2.10/1.60 tff(127,plain,
% 2.10/1.60 (![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)))),
% 2.10/1.60 inference(quant_intro,[status(thm)],[126])).
% 2.10/1.60 tff(128,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/sandbox2/benchmark/Axioms/PLA001-0.ax','putdown_1')).
% 2.10/1.60 tff(129,plain,
% 2.10/1.60 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[128, 127])).
% 2.10/1.60 tff(130,plain,
% 2.10/1.60 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[129, 125])).
% 2.10/1.60 tff(131,plain,(
% 2.10/1.60 ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 2.10/1.60 inference(skolemize,[status(sab)],[130])).
% 2.10/1.60 tff(132,plain,
% 2.10/1.60 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[131, 124])).
% 2.10/1.60 tff(133,plain,
% 2.10/1.60 (((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | ((~holds(clear(d), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(empty, do(putdown(c, d), 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(d), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(empty, do(putdown(c, d), do(pickup(c), s0))))),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(134,plain,
% 2.10/1.60 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | ((~holds(clear(d), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(empty, do(putdown(c, d), do(pickup(c), s0))))),
% 2.10/1.60 inference(quant_inst,[status(thm)],[])).
% 2.10/1.60 tff(135,plain,
% 2.10/1.60 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | (~holds(clear(d), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(empty, do(putdown(c, d), do(pickup(c), s0)))),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[134, 133])).
% 2.10/1.60 tff(136,plain,
% 2.10/1.60 (holds(empty, do(putdown(c, d), do(pickup(c), s0)))),
% 2.10/1.60 inference(unit_resolution,[status(thm)],[135, 132, 46, 26])).
% 2.10/1.60 tff(137,plain,
% 2.10/1.60 (differ(a, table) <=> differ(a, table)),
% 2.10/1.60 inference(rewrite,[status(thm)],[])).
% 2.10/1.60 tff(138,axiom,(differ(a, table)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','differ_a_table')).
% 2.10/1.60 tff(139,plain,
% 2.10/1.60 (differ(a, table)),
% 2.10/1.60 inference(modus_ponens,[status(thm)],[138, 137])).
% 2.10/1.60 tff(140,plain,
% 2.10/1.60 (((~![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, d), do(pickup(c), s0)))) | (~holds(clear(a), do(putdown(c, d), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, d), 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, d), do(pickup(c), s0)))) | (~holds(clear(a), do(putdown(c, d), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, d), do(pickup(c), s0)))))),
% 2.10/1.61 inference(rewrite,[status(thm)],[])).
% 2.10/1.61 tff(141,plain,
% 2.10/1.61 (((~differ(a, table)) | (~holds(clear(a), do(putdown(c, d), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, d), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, d), do(pickup(c), s0))))) <=> ((~differ(a, table)) | (~holds(empty, do(putdown(c, d), do(pickup(c), s0)))) | (~holds(clear(a), do(putdown(c, d), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, d), do(pickup(c), s0)))))),
% 2.10/1.61 inference(rewrite,[status(thm)],[])).
% 2.10/1.61 tff(142,plain,
% 2.10/1.61 (((~![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, d), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, d), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, d), 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, d), do(pickup(c), s0)))) | (~holds(clear(a), do(putdown(c, d), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, d), do(pickup(c), s0))))))),
% 2.10/1.61 inference(monotonicity,[status(thm)],[141])).
% 2.10/1.61 tff(143,plain,
% 2.10/1.61 (((~![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, d), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, d), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, d), 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, d), do(pickup(c), s0)))) | (~holds(clear(a), do(putdown(c, d), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, d), do(pickup(c), s0)))))),
% 2.10/1.61 inference(transitivity,[status(thm)],[142, 140])).
% 2.10/1.61 tff(144,plain,
% 2.10/1.61 ((~![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, d), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, d), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, d), do(pickup(c), s0)))))),
% 2.10/1.61 inference(quant_inst,[status(thm)],[])).
% 2.10/1.61 tff(145,plain,
% 2.10/1.61 ((~![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, d), do(pickup(c), s0)))) | (~holds(clear(a), do(putdown(c, d), do(pickup(c), s0)))) | holds(holding(a), do(pickup(a), do(putdown(c, d), do(pickup(c), s0))))),
% 2.10/1.61 inference(modus_ponens,[status(thm)],[144, 143])).
% 2.10/1.61 tff(146,plain,
% 2.10/1.61 (holds(holding(a), do(pickup(a), do(putdown(c, d), do(pickup(c), s0))))),
% 2.10/1.61 inference(unit_resolution,[status(thm)],[145, 19, 139, 136, 122])).
% 2.10/1.61 tff(147,plain,
% 2.10/1.61 (^[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))))),
% 2.10/1.61 inference(bind,[status(th)],[])).
% 2.10/1.61 tff(148,plain,
% 2.10/1.61 (![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)))),
% 2.10/1.61 inference(quant_intro,[status(thm)],[147])).
% 2.10/1.61 tff(149,plain,
% 2.10/1.61 (![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)))),
% 2.10/1.61 inference(rewrite,[status(thm)],[])).
% 2.10/1.61 tff(150,plain,
% 2.10/1.61 (^[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)))))),
% 2.10/1.61 inference(bind,[status(th)],[])).
% 2.10/1.61 tff(151,plain,
% 2.10/1.61 (![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)))),
% 2.10/1.61 inference(quant_intro,[status(thm)],[150])).
% 2.10/1.61 tff(152,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/sandbox2/benchmark/Axioms/PLA001-0.ax','putdown_2')).
% 2.10/1.61 tff(153,plain,
% 2.10/1.61 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 2.10/1.61 inference(modus_ponens,[status(thm)],[152, 151])).
% 2.10/1.61 tff(154,plain,
% 2.10/1.61 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 2.10/1.61 inference(modus_ponens,[status(thm)],[153, 149])).
% 2.10/1.61 tff(155,plain,(
% 2.10/1.61 ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 2.10/1.61 inference(skolemize,[status(sab)],[154])).
% 2.10/1.61 tff(156,plain,
% 2.10/1.61 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 2.10/1.61 inference(modus_ponens,[status(thm)],[155, 148])).
% 2.10/1.61 tff(157,plain,
% 2.10/1.61 (((~![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(c), do(pickup(a), do(putdown(c, d), do(pickup(c), s0))))) | (~holds(holding(a), do(pickup(a), do(putdown(c, d), do(pickup(c), s0))))) | holds(on(a, c), do(putdown(a, c), do(pickup(a), do(putdown(c, d), 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(c), do(pickup(a), do(putdown(c, d), do(pickup(c), s0))))) | (~holds(holding(a), do(pickup(a), do(putdown(c, d), do(pickup(c), s0))))) | holds(on(a, c), do(putdown(a, c), do(pickup(a), do(putdown(c, d), do(pickup(c), s0))))))),
% 2.10/1.61 inference(rewrite,[status(thm)],[])).
% 2.10/1.61 tff(158,plain,
% 2.10/1.61 ((~![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(c), do(pickup(a), do(putdown(c, d), do(pickup(c), s0))))) | (~holds(holding(a), do(pickup(a), do(putdown(c, d), do(pickup(c), s0))))) | holds(on(a, c), do(putdown(a, c), do(pickup(a), do(putdown(c, d), do(pickup(c), s0))))))),
% 2.10/1.61 inference(quant_inst,[status(thm)],[])).
% 2.10/1.61 tff(159,plain,
% 2.10/1.61 ((~![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(c), do(pickup(a), do(putdown(c, d), do(pickup(c), s0))))) | (~holds(holding(a), do(pickup(a), do(putdown(c, d), do(pickup(c), s0))))) | holds(on(a, c), do(putdown(a, c), do(pickup(a), do(putdown(c, d), do(pickup(c), s0)))))),
% 2.10/1.61 inference(modus_ponens,[status(thm)],[158, 157])).
% 2.10/1.61 tff(160,plain,
% 2.10/1.61 (holds(on(a, c), do(putdown(a, c), do(pickup(a), do(putdown(c, d), do(pickup(c), s0)))))),
% 2.10/1.61 inference(unit_resolution,[status(thm)],[159, 156, 146, 94])).
% 2.10/1.61 tff(161,plain,
% 2.10/1.61 (^[State: $i] : refl((~holds(on(a, c), State)) <=> (~holds(on(a, c), State)))),
% 2.10/1.61 inference(bind,[status(th)],[])).
% 2.10/1.61 tff(162,plain,
% 2.10/1.61 (![State: $i] : (~holds(on(a, c), State)) <=> ![State: $i] : (~holds(on(a, c), State))),
% 2.10/1.61 inference(quant_intro,[status(thm)],[161])).
% 2.10/1.61 tff(163,plain,
% 2.10/1.61 (![State: $i] : (~holds(on(a, c), State)) <=> ![State: $i] : (~holds(on(a, c), State))),
% 2.10/1.61 inference(rewrite,[status(thm)],[])).
% 2.10/1.61 tff(164,axiom,(![State: $i] : (~holds(on(a, c), State))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_AC')).
% 2.10/1.61 tff(165,plain,
% 2.10/1.61 (![State: $i] : (~holds(on(a, c), State))),
% 2.10/1.61 inference(modus_ponens,[status(thm)],[164, 163])).
% 2.10/1.61 tff(166,plain,(
% 2.10/1.61 ![State: $i] : (~holds(on(a, c), State))),
% 2.10/1.61 inference(skolemize,[status(sab)],[165])).
% 2.10/1.61 tff(167,plain,
% 2.10/1.61 (![State: $i] : (~holds(on(a, c), State))),
% 2.10/1.61 inference(modus_ponens,[status(thm)],[166, 162])).
% 2.10/1.61 tff(168,plain,
% 2.10/1.61 ((~![State: $i] : (~holds(on(a, c), State))) | (~holds(on(a, c), do(putdown(a, c), do(pickup(a), do(putdown(c, d), do(pickup(c), s0))))))),
% 2.10/1.61 inference(quant_inst,[status(thm)],[])).
% 2.10/1.61 tff(169,plain,
% 2.10/1.61 ($false),
% 2.10/1.61 inference(unit_resolution,[status(thm)],[168, 167, 160])).
% 2.10/1.61 % SZS output end Proof
%------------------------------------------------------------------------------