TSTP Solution File: PLA019-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PLA019-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 127.75s 82.19s
% Output : Proof 127.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PLA019-1 : TPTP v8.1.0. Released v1.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 17:29:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 127.75/82.19 % SZS status Unsatisfiable
% 127.75/82.19 % SZS output start Proof
% 127.75/82.19 tff(holds_type, type, (
% 127.75/82.19 holds: ( $i * $i ) > $o)).
% 127.75/82.19 tff(do_type, type, (
% 127.75/82.19 do: ( $i * $i ) > $i)).
% 127.75/82.19 tff(s0_type, type, (
% 127.75/82.19 s0: $i)).
% 127.75/82.19 tff(pickup_type, type, (
% 127.75/82.19 pickup: $i > $i)).
% 127.75/82.19 tff(c_type, type, (
% 127.75/82.19 c: $i)).
% 127.75/82.19 tff(putdown_type, type, (
% 127.75/82.19 putdown: ( $i * $i ) > $i)).
% 127.75/82.19 tff(a_type, type, (
% 127.75/82.19 a: $i)).
% 127.75/82.19 tff(d_type, type, (
% 127.75/82.19 d: $i)).
% 127.75/82.19 tff(on_type, type, (
% 127.75/82.19 on: ( $i * $i ) > $i)).
% 127.75/82.19 tff(clear_type, type, (
% 127.75/82.19 clear: $i > $i)).
% 127.75/82.19 tff(differ_type, type, (
% 127.75/82.19 differ: ( $i * $i ) > $o)).
% 127.75/82.19 tff(holding_type, type, (
% 127.75/82.19 holding: $i > $i)).
% 127.75/82.19 tff(empty_type, type, (
% 127.75/82.19 empty: $i)).
% 127.75/82.19 tff(table_type, type, (
% 127.75/82.19 table: $i)).
% 127.75/82.19 tff(1,assumption,(~holds(clear(c), do(pickup(d), do(putdown(c, a), do(pickup(c), s0))))), introduced(assumption)).
% 127.75/82.19 tff(2,assumption,(~holds(clear(a), do(pickup(c), s0))), introduced(assumption)).
% 127.75/82.19 tff(3,plain,
% 127.75/82.19 (holds(clear(a), s0) <=> holds(clear(a), s0)),
% 127.75/82.19 inference(rewrite,[status(thm)],[])).
% 127.75/82.19 tff(4,axiom,(holds(clear(a), s0)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','initial_state5')).
% 127.75/82.19 tff(5,plain,
% 127.75/82.19 (holds(clear(a), s0)),
% 127.75/82.19 inference(modus_ponens,[status(thm)],[4, 3])).
% 127.75/82.19 tff(6,plain,
% 127.75/82.19 (differ(a, c) <=> differ(a, c)),
% 127.75/82.19 inference(rewrite,[status(thm)],[])).
% 127.75/82.19 tff(7,axiom,(differ(a, c)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','differ_a_c')).
% 127.75/82.19 tff(8,plain,
% 127.75/82.19 (differ(a, c)),
% 127.75/82.19 inference(modus_ponens,[status(thm)],[7, 6])).
% 127.75/82.19 tff(9,plain,
% 127.75/82.19 (^[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))))),
% 127.75/82.19 inference(bind,[status(th)],[])).
% 127.75/82.19 tff(10,plain,
% 127.75/82.19 (![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)))),
% 127.75/82.19 inference(quant_intro,[status(thm)],[9])).
% 127.75/82.19 tff(11,plain,
% 127.75/82.19 (![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)))),
% 127.75/82.19 inference(rewrite,[status(thm)],[])).
% 127.75/82.19 tff(12,plain,
% 127.75/82.19 (^[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)))))),
% 127.75/82.19 inference(bind,[status(th)],[])).
% 127.75/82.19 tff(13,plain,
% 127.75/82.19 (![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)))),
% 127.75/82.19 inference(quant_intro,[status(thm)],[12])).
% 127.75/82.19 tff(14,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')).
% 127.75/82.19 tff(15,plain,
% 127.75/82.19 (![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 127.75/82.19 inference(modus_ponens,[status(thm)],[14, 13])).
% 127.75/82.19 tff(16,plain,
% 127.75/82.19 (![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 127.75/82.19 inference(modus_ponens,[status(thm)],[15, 11])).
% 127.75/82.19 tff(17,plain,(
% 127.75/82.19 ![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 127.75/82.19 inference(skolemize,[status(sab)],[16])).
% 127.75/82.19 tff(18,plain,
% 127.75/82.19 (![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 127.75/82.19 inference(modus_ponens,[status(thm)],[17, 10])).
% 127.75/82.19 tff(19,plain,
% 127.75/82.19 (((~![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)))),
% 127.75/82.19 inference(rewrite,[status(thm)],[])).
% 127.75/82.19 tff(20,plain,
% 127.75/82.19 ((~![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)))),
% 127.75/82.19 inference(quant_inst,[status(thm)],[])).
% 127.75/82.19 tff(21,plain,
% 127.75/82.19 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~holds(clear(a), s0)) | (~differ(a, c)) | holds(clear(a), do(pickup(c), s0))),
% 127.75/82.19 inference(modus_ponens,[status(thm)],[20, 19])).
% 127.75/82.19 tff(22,plain,
% 127.75/82.19 ($false),
% 127.75/82.19 inference(unit_resolution,[status(thm)],[21, 18, 8, 5, 2])).
% 127.75/82.19 tff(23,plain,(holds(clear(a), do(pickup(c), s0))), inference(lemma,lemma(discharge,[]))).
% 127.75/82.19 tff(24,plain,
% 127.75/82.19 (holds(empty, s0) <=> holds(empty, s0)),
% 127.75/82.19 inference(rewrite,[status(thm)],[])).
% 127.75/82.19 tff(25,axiom,(holds(empty, s0)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','initial_state8')).
% 127.75/82.19 tff(26,plain,
% 127.75/82.19 (holds(empty, s0)),
% 127.75/82.19 inference(modus_ponens,[status(thm)],[25, 24])).
% 127.75/82.19 tff(27,plain,
% 127.75/82.19 (holds(clear(c), s0) <=> holds(clear(c), s0)),
% 127.75/82.19 inference(rewrite,[status(thm)],[])).
% 127.75/82.19 tff(28,axiom,(holds(clear(c), s0)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','initial_state7')).
% 127.75/82.19 tff(29,plain,
% 127.75/82.19 (holds(clear(c), s0)),
% 127.75/82.19 inference(modus_ponens,[status(thm)],[28, 27])).
% 127.75/82.19 tff(30,plain,
% 127.75/82.19 (differ(c, table) <=> differ(c, table)),
% 127.75/82.19 inference(rewrite,[status(thm)],[])).
% 127.75/82.19 tff(31,axiom,(differ(c, table)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','differ_c_table')).
% 127.75/82.19 tff(32,plain,
% 127.75/82.19 (differ(c, table)),
% 127.75/82.19 inference(modus_ponens,[status(thm)],[31, 30])).
% 127.75/82.19 tff(33,plain,
% 127.75/82.19 (^[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))))),
% 127.75/82.19 inference(bind,[status(th)],[])).
% 127.75/82.19 tff(34,plain,
% 127.75/82.19 (![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)))),
% 127.75/82.19 inference(quant_intro,[status(thm)],[33])).
% 127.75/82.19 tff(35,plain,
% 127.75/82.19 (![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)))),
% 127.75/82.19 inference(rewrite,[status(thm)],[])).
% 127.75/82.19 tff(36,plain,
% 127.75/82.19 (^[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)))))),
% 127.75/82.19 inference(bind,[status(th)],[])).
% 127.75/82.19 tff(37,plain,
% 127.75/82.19 (![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)))),
% 127.75/82.19 inference(quant_intro,[status(thm)],[36])).
% 127.75/82.19 tff(38,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')).
% 127.75/82.19 tff(39,plain,
% 127.75/82.19 (![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 127.75/82.19 inference(modus_ponens,[status(thm)],[38, 37])).
% 127.75/82.19 tff(40,plain,
% 127.75/82.19 (![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 127.75/82.19 inference(modus_ponens,[status(thm)],[39, 35])).
% 127.75/82.19 tff(41,plain,(
% 127.75/82.19 ![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 127.75/82.19 inference(skolemize,[status(sab)],[40])).
% 127.75/82.19 tff(42,plain,
% 127.75/82.19 (![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 127.75/82.19 inference(modus_ponens,[status(thm)],[41, 34])).
% 127.75/82.19 tff(43,plain,
% 127.75/82.19 (((~![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)))),
% 127.75/82.19 inference(rewrite,[status(thm)],[])).
% 127.75/82.19 tff(44,plain,
% 127.75/82.19 (((~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)))),
% 127.75/82.19 inference(rewrite,[status(thm)],[])).
% 127.75/82.19 tff(45,plain,
% 127.75/82.19 (((~![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))))),
% 127.75/82.19 inference(monotonicity,[status(thm)],[44])).
% 127.75/82.19 tff(46,plain,
% 127.75/82.19 (((~![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)))),
% 127.75/82.20 inference(transitivity,[status(thm)],[45, 43])).
% 127.75/82.20 tff(47,plain,
% 127.75/82.20 ((~![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)))),
% 127.75/82.20 inference(quant_inst,[status(thm)],[])).
% 127.75/82.20 tff(48,plain,
% 127.75/82.20 ((~![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))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[47, 46])).
% 127.75/82.20 tff(49,plain,
% 127.75/82.20 (holds(holding(c), do(pickup(c), s0))),
% 127.75/82.20 inference(unit_resolution,[status(thm)],[48, 42, 32, 29, 26])).
% 127.75/82.20 tff(50,plain,
% 127.75/82.20 (^[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))))),
% 127.75/82.20 inference(bind,[status(th)],[])).
% 127.75/82.20 tff(51,plain,
% 127.75/82.20 (![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)))),
% 127.75/82.20 inference(quant_intro,[status(thm)],[50])).
% 127.75/82.20 tff(52,plain,
% 127.75/82.20 (![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)))),
% 127.75/82.20 inference(rewrite,[status(thm)],[])).
% 127.75/82.20 tff(53,plain,
% 127.75/82.20 (^[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)))))),
% 127.75/82.20 inference(bind,[status(th)],[])).
% 127.75/82.20 tff(54,plain,
% 127.75/82.20 (![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)))),
% 127.75/82.20 inference(quant_intro,[status(thm)],[53])).
% 127.75/82.20 tff(55,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')).
% 127.75/82.20 tff(56,plain,
% 127.75/82.20 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[55, 54])).
% 127.75/82.20 tff(57,plain,
% 127.75/82.20 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[56, 52])).
% 127.75/82.20 tff(58,plain,(
% 127.75/82.20 ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 127.75/82.20 inference(skolemize,[status(sab)],[57])).
% 127.75/82.20 tff(59,plain,
% 127.75/82.20 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[58, 51])).
% 127.75/82.20 tff(60,plain,
% 127.75/82.20 (((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | ((~holds(clear(a), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(clear(c), do(putdown(c, a), 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(a), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(clear(c), do(putdown(c, a), do(pickup(c), s0))))),
% 127.75/82.20 inference(rewrite,[status(thm)],[])).
% 127.75/82.20 tff(61,plain,
% 127.75/82.20 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | ((~holds(clear(a), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(clear(c), do(putdown(c, a), do(pickup(c), s0))))),
% 127.75/82.20 inference(quant_inst,[status(thm)],[])).
% 127.75/82.20 tff(62,plain,
% 127.75/82.20 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | (~holds(clear(a), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(clear(c), do(putdown(c, a), do(pickup(c), s0)))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[61, 60])).
% 127.75/82.20 tff(63,plain,
% 127.75/82.20 (holds(clear(c), do(putdown(c, a), do(pickup(c), s0)))),
% 127.75/82.20 inference(unit_resolution,[status(thm)],[62, 59, 49, 23])).
% 127.75/82.20 tff(64,plain,
% 127.75/82.20 (differ(c, d) <=> differ(c, d)),
% 127.75/82.20 inference(rewrite,[status(thm)],[])).
% 127.75/82.20 tff(65,axiom,(differ(c, d)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','differ_c_d')).
% 127.75/82.20 tff(66,plain,
% 127.75/82.20 (differ(c, d)),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[65, 64])).
% 127.75/82.20 tff(67,plain,
% 127.75/82.20 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~differ(c, d)) | (~holds(clear(c), do(putdown(c, a), do(pickup(c), s0)))) | holds(clear(c), do(pickup(d), do(putdown(c, 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)))) | (~differ(c, d)) | (~holds(clear(c), do(putdown(c, a), do(pickup(c), s0)))) | holds(clear(c), do(pickup(d), do(putdown(c, a), do(pickup(c), s0)))))),
% 127.75/82.20 inference(rewrite,[status(thm)],[])).
% 127.75/82.20 tff(68,plain,
% 127.75/82.20 (((~holds(clear(c), do(putdown(c, a), do(pickup(c), s0)))) | (~differ(c, d)) | holds(clear(c), do(pickup(d), do(putdown(c, a), do(pickup(c), s0))))) <=> ((~differ(c, d)) | (~holds(clear(c), do(putdown(c, a), do(pickup(c), s0)))) | holds(clear(c), do(pickup(d), do(putdown(c, a), do(pickup(c), s0)))))),
% 127.75/82.20 inference(rewrite,[status(thm)],[])).
% 127.75/82.20 tff(69,plain,
% 127.75/82.20 (((~![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, a), do(pickup(c), s0)))) | (~differ(c, d)) | holds(clear(c), do(pickup(d), do(putdown(c, 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)))) | ((~differ(c, d)) | (~holds(clear(c), do(putdown(c, a), do(pickup(c), s0)))) | holds(clear(c), do(pickup(d), do(putdown(c, a), do(pickup(c), s0))))))),
% 127.75/82.20 inference(monotonicity,[status(thm)],[68])).
% 127.75/82.20 tff(70,plain,
% 127.75/82.20 (((~![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, a), do(pickup(c), s0)))) | (~differ(c, d)) | holds(clear(c), do(pickup(d), do(putdown(c, 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)))) | (~differ(c, d)) | (~holds(clear(c), do(putdown(c, a), do(pickup(c), s0)))) | holds(clear(c), do(pickup(d), do(putdown(c, a), do(pickup(c), s0)))))),
% 127.75/82.20 inference(transitivity,[status(thm)],[69, 67])).
% 127.75/82.20 tff(71,plain,
% 127.75/82.20 ((~![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, a), do(pickup(c), s0)))) | (~differ(c, d)) | holds(clear(c), do(pickup(d), do(putdown(c, a), do(pickup(c), s0)))))),
% 127.75/82.20 inference(quant_inst,[status(thm)],[])).
% 127.75/82.20 tff(72,plain,
% 127.75/82.20 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~differ(c, d)) | (~holds(clear(c), do(putdown(c, a), do(pickup(c), s0)))) | holds(clear(c), do(pickup(d), do(putdown(c, a), do(pickup(c), s0))))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[71, 70])).
% 127.75/82.20 tff(73,plain,
% 127.75/82.20 ($false),
% 127.75/82.20 inference(unit_resolution,[status(thm)],[72, 18, 66, 63, 1])).
% 127.75/82.20 tff(74,plain,(holds(clear(c), do(pickup(d), do(putdown(c, a), do(pickup(c), s0))))), inference(lemma,lemma(discharge,[]))).
% 127.75/82.20 tff(75,plain,
% 127.75/82.20 (differ(a, d) <=> differ(a, d)),
% 127.75/82.20 inference(rewrite,[status(thm)],[])).
% 127.75/82.20 tff(76,axiom,(differ(a, d)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','differ_a_d')).
% 127.75/82.20 tff(77,plain,
% 127.75/82.20 (differ(a, d)),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[76, 75])).
% 127.75/82.20 tff(78,plain,
% 127.75/82.20 (^[Y: $i, X: $i] : refl(((~differ(Y, X)) | differ(X, Y)) <=> ((~differ(Y, X)) | differ(X, Y)))),
% 127.75/82.20 inference(bind,[status(th)],[])).
% 127.75/82.20 tff(79,plain,
% 127.75/82.20 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y)) <=> ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 127.75/82.20 inference(quant_intro,[status(thm)],[78])).
% 127.75/82.20 tff(80,plain,
% 127.75/82.20 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y)) <=> ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 127.75/82.20 inference(rewrite,[status(thm)],[])).
% 127.75/82.20 tff(81,plain,
% 127.75/82.20 (^[Y: $i, X: $i] : rewrite((differ(X, Y) | (~differ(Y, X))) <=> ((~differ(Y, X)) | differ(X, Y)))),
% 127.75/82.20 inference(bind,[status(th)],[])).
% 127.75/82.20 tff(82,plain,
% 127.75/82.20 (![Y: $i, X: $i] : (differ(X, Y) | (~differ(Y, X))) <=> ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 127.75/82.20 inference(quant_intro,[status(thm)],[81])).
% 127.75/82.20 tff(83,axiom,(![Y: $i, X: $i] : (differ(X, Y) | (~differ(Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','symmetry_of_differ')).
% 127.75/82.20 tff(84,plain,
% 127.75/82.20 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[83, 82])).
% 127.75/82.20 tff(85,plain,
% 127.75/82.20 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[84, 80])).
% 127.75/82.20 tff(86,plain,(
% 127.75/82.20 ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 127.75/82.20 inference(skolemize,[status(sab)],[85])).
% 127.75/82.20 tff(87,plain,
% 127.75/82.20 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[86, 79])).
% 127.75/82.20 tff(88,plain,
% 127.75/82.20 (((~![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))),
% 127.75/82.20 inference(rewrite,[status(thm)],[])).
% 127.75/82.20 tff(89,plain,
% 127.75/82.20 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | ((~differ(a, d)) | differ(d, a))),
% 127.75/82.20 inference(quant_inst,[status(thm)],[])).
% 127.75/82.20 tff(90,plain,
% 127.75/82.20 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | (~differ(a, d)) | differ(d, a)),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[89, 88])).
% 127.75/82.20 tff(91,plain,
% 127.75/82.20 (differ(d, a)),
% 127.75/82.20 inference(unit_resolution,[status(thm)],[90, 87, 77])).
% 127.75/82.20 tff(92,plain,
% 127.75/82.20 (holds(on(c, d), s0) <=> holds(on(c, d), s0)),
% 127.75/82.20 inference(rewrite,[status(thm)],[])).
% 127.75/82.20 tff(93,axiom,(holds(on(c, d), s0)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','initial_state3')).
% 127.75/82.20 tff(94,plain,
% 127.75/82.20 (holds(on(c, d), s0)),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[93, 92])).
% 127.75/82.20 tff(95,plain,
% 127.75/82.20 (^[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))))),
% 127.75/82.20 inference(bind,[status(th)],[])).
% 127.75/82.20 tff(96,plain,
% 127.75/82.20 (![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)))),
% 127.75/82.20 inference(quant_intro,[status(thm)],[95])).
% 127.75/82.20 tff(97,plain,
% 127.75/82.20 (![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)))),
% 127.75/82.20 inference(rewrite,[status(thm)],[])).
% 127.75/82.20 tff(98,plain,
% 127.75/82.20 (^[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)))))),
% 127.75/82.20 inference(bind,[status(th)],[])).
% 127.75/82.20 tff(99,plain,
% 127.75/82.20 (![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)))),
% 127.75/82.20 inference(quant_intro,[status(thm)],[98])).
% 127.75/82.20 tff(100,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')).
% 127.75/82.20 tff(101,plain,
% 127.75/82.20 (![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)))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[100, 99])).
% 127.75/82.20 tff(102,plain,
% 127.75/82.20 (![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)))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[101, 97])).
% 127.75/82.20 tff(103,plain,(
% 127.75/82.20 ![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)))),
% 127.75/82.20 inference(skolemize,[status(sab)],[102])).
% 127.75/82.20 tff(104,plain,
% 127.75/82.20 (![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)))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[103, 96])).
% 127.75/82.20 tff(105,plain,
% 127.75/82.20 (((~![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)))),
% 127.75/82.20 inference(rewrite,[status(thm)],[])).
% 127.75/82.20 tff(106,plain,
% 127.75/82.20 (((~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)))),
% 127.75/82.20 inference(rewrite,[status(thm)],[])).
% 127.75/82.20 tff(107,plain,
% 127.75/82.20 (((~![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))))),
% 127.75/82.20 inference(monotonicity,[status(thm)],[106])).
% 127.75/82.20 tff(108,plain,
% 127.75/82.20 (((~![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)))),
% 127.75/82.20 inference(transitivity,[status(thm)],[107, 105])).
% 127.75/82.20 tff(109,plain,
% 127.75/82.20 ((~![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)))),
% 127.75/82.20 inference(quant_inst,[status(thm)],[])).
% 127.75/82.20 tff(110,plain,
% 127.75/82.20 ((~![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))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[109, 108])).
% 127.75/82.20 tff(111,plain,
% 127.75/82.20 (holds(clear(d), do(pickup(c), s0))),
% 127.75/82.20 inference(unit_resolution,[status(thm)],[110, 104, 94, 29, 26])).
% 127.75/82.20 tff(112,plain,
% 127.75/82.20 (^[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))))),
% 127.75/82.20 inference(bind,[status(th)],[])).
% 127.75/82.20 tff(113,plain,
% 127.75/82.20 (![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)))),
% 127.75/82.20 inference(quant_intro,[status(thm)],[112])).
% 127.75/82.20 tff(114,plain,
% 127.75/82.20 (![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)))),
% 127.75/82.20 inference(rewrite,[status(thm)],[])).
% 127.75/82.20 tff(115,plain,
% 127.75/82.20 (^[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)))))),
% 127.75/82.20 inference(bind,[status(th)],[])).
% 127.75/82.20 tff(116,plain,
% 127.75/82.20 (![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)))),
% 127.75/82.20 inference(quant_intro,[status(thm)],[115])).
% 127.75/82.20 tff(117,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')).
% 127.75/82.20 tff(118,plain,
% 127.75/82.20 (![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[117, 116])).
% 127.75/82.20 tff(119,plain,
% 127.75/82.20 (![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[118, 114])).
% 127.75/82.20 tff(120,plain,(
% 127.75/82.20 ![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 127.75/82.20 inference(skolemize,[status(sab)],[119])).
% 127.75/82.20 tff(121,plain,
% 127.75/82.20 (![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[120, 113])).
% 127.75/82.20 tff(122,plain,
% 127.75/82.20 (((~![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, a)) | (~holds(clear(d), do(pickup(c), s0))) | holds(clear(d), do(putdown(c, a), 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, a)) | (~holds(clear(d), do(pickup(c), s0))) | holds(clear(d), do(putdown(c, a), do(pickup(c), s0))))),
% 127.75/82.20 inference(rewrite,[status(thm)],[])).
% 127.75/82.20 tff(123,plain,
% 127.75/82.20 ((~![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, a)) | (~holds(clear(d), do(pickup(c), s0))) | holds(clear(d), do(putdown(c, a), do(pickup(c), s0))))),
% 127.75/82.20 inference(quant_inst,[status(thm)],[])).
% 127.75/82.20 tff(124,plain,
% 127.75/82.20 ((~![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, a)) | (~holds(clear(d), do(pickup(c), s0))) | holds(clear(d), do(putdown(c, a), do(pickup(c), s0)))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[123, 122])).
% 127.75/82.20 tff(125,plain,
% 127.75/82.20 (holds(clear(d), do(putdown(c, a), do(pickup(c), s0)))),
% 127.75/82.20 inference(unit_resolution,[status(thm)],[124, 121, 111, 91])).
% 127.75/82.20 tff(126,plain,
% 127.75/82.20 (^[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))))),
% 127.75/82.20 inference(bind,[status(th)],[])).
% 127.75/82.20 tff(127,plain,
% 127.75/82.20 (![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)))),
% 127.75/82.20 inference(quant_intro,[status(thm)],[126])).
% 127.75/82.20 tff(128,plain,
% 127.75/82.20 (![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)))),
% 127.75/82.20 inference(rewrite,[status(thm)],[])).
% 127.75/82.20 tff(129,plain,
% 127.75/82.20 (^[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)))))),
% 127.75/82.20 inference(bind,[status(th)],[])).
% 127.75/82.20 tff(130,plain,
% 127.75/82.20 (![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)))),
% 127.75/82.20 inference(quant_intro,[status(thm)],[129])).
% 127.75/82.20 tff(131,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')).
% 127.75/82.20 tff(132,plain,
% 127.75/82.20 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[131, 130])).
% 127.75/82.20 tff(133,plain,
% 127.75/82.20 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[132, 128])).
% 127.75/82.20 tff(134,plain,(
% 127.75/82.20 ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 127.75/82.20 inference(skolemize,[status(sab)],[133])).
% 127.75/82.20 tff(135,plain,
% 127.75/82.20 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[134, 127])).
% 127.75/82.20 tff(136,plain,
% 127.75/82.20 (((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | ((~holds(clear(a), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(empty, do(putdown(c, a), 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(a), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(empty, do(putdown(c, a), do(pickup(c), s0))))),
% 127.75/82.20 inference(rewrite,[status(thm)],[])).
% 127.75/82.20 tff(137,plain,
% 127.75/82.20 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | ((~holds(clear(a), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(empty, do(putdown(c, a), do(pickup(c), s0))))),
% 127.75/82.20 inference(quant_inst,[status(thm)],[])).
% 127.75/82.20 tff(138,plain,
% 127.75/82.20 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | (~holds(clear(a), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(empty, do(putdown(c, a), do(pickup(c), s0)))),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[137, 136])).
% 127.75/82.20 tff(139,plain,
% 127.75/82.20 (holds(empty, do(putdown(c, a), do(pickup(c), s0)))),
% 127.75/82.20 inference(unit_resolution,[status(thm)],[138, 135, 49, 23])).
% 127.75/82.20 tff(140,plain,
% 127.75/82.20 (differ(d, table) <=> differ(d, table)),
% 127.75/82.20 inference(rewrite,[status(thm)],[])).
% 127.75/82.20 tff(141,axiom,(differ(d, table)), file('/export/starexec/sandbox/benchmark/Axioms/PLA001-1.ax','differ_d_table')).
% 127.75/82.20 tff(142,plain,
% 127.75/82.20 (differ(d, table)),
% 127.75/82.20 inference(modus_ponens,[status(thm)],[141, 140])).
% 127.75/82.20 tff(143,plain,
% 127.75/82.20 (((~![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(c, a), do(pickup(c), s0)))) | (~holds(clear(d), do(putdown(c, a), do(pickup(c), s0)))) | holds(holding(d), do(pickup(d), do(putdown(c, a), 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(c, a), do(pickup(c), s0)))) | (~holds(clear(d), do(putdown(c, a), do(pickup(c), s0)))) | holds(holding(d), do(pickup(d), do(putdown(c, a), do(pickup(c), s0)))))),
% 127.75/82.21 inference(rewrite,[status(thm)],[])).
% 127.75/82.21 tff(144,plain,
% 127.75/82.21 (((~differ(d, table)) | (~holds(clear(d), do(putdown(c, a), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, a), do(pickup(c), s0)))) | holds(holding(d), do(pickup(d), do(putdown(c, a), do(pickup(c), s0))))) <=> ((~differ(d, table)) | (~holds(empty, do(putdown(c, a), do(pickup(c), s0)))) | (~holds(clear(d), do(putdown(c, a), do(pickup(c), s0)))) | holds(holding(d), do(pickup(d), do(putdown(c, a), do(pickup(c), s0)))))),
% 127.75/82.21 inference(rewrite,[status(thm)],[])).
% 127.75/82.21 tff(145,plain,
% 127.75/82.21 (((~![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(c, a), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, a), do(pickup(c), s0)))) | holds(holding(d), do(pickup(d), do(putdown(c, a), 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(c, a), do(pickup(c), s0)))) | (~holds(clear(d), do(putdown(c, a), do(pickup(c), s0)))) | holds(holding(d), do(pickup(d), do(putdown(c, a), do(pickup(c), s0))))))),
% 127.75/82.21 inference(monotonicity,[status(thm)],[144])).
% 127.75/82.21 tff(146,plain,
% 127.75/82.21 (((~![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(c, a), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, a), do(pickup(c), s0)))) | holds(holding(d), do(pickup(d), do(putdown(c, a), 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(c, a), do(pickup(c), s0)))) | (~holds(clear(d), do(putdown(c, a), do(pickup(c), s0)))) | holds(holding(d), do(pickup(d), do(putdown(c, a), do(pickup(c), s0)))))),
% 127.75/82.21 inference(transitivity,[status(thm)],[145, 143])).
% 127.75/82.21 tff(147,plain,
% 127.75/82.21 ((~![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(c, a), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, a), do(pickup(c), s0)))) | holds(holding(d), do(pickup(d), do(putdown(c, a), do(pickup(c), s0)))))),
% 127.75/82.21 inference(quant_inst,[status(thm)],[])).
% 127.75/82.21 tff(148,plain,
% 127.75/82.21 ((~![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(c, a), do(pickup(c), s0)))) | (~holds(clear(d), do(putdown(c, a), do(pickup(c), s0)))) | holds(holding(d), do(pickup(d), do(putdown(c, a), do(pickup(c), s0))))),
% 127.75/82.21 inference(modus_ponens,[status(thm)],[147, 146])).
% 127.75/82.21 tff(149,plain,
% 127.75/82.21 (holds(holding(d), do(pickup(d), do(putdown(c, a), do(pickup(c), s0))))),
% 127.75/82.21 inference(unit_resolution,[status(thm)],[148, 42, 142, 139, 125])).
% 127.75/82.21 tff(150,plain,
% 127.75/82.21 (^[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))))),
% 127.75/82.21 inference(bind,[status(th)],[])).
% 127.75/82.21 tff(151,plain,
% 127.75/82.21 (![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)))),
% 127.75/82.21 inference(quant_intro,[status(thm)],[150])).
% 127.75/82.21 tff(152,plain,
% 127.75/82.21 (![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)))),
% 127.75/82.21 inference(rewrite,[status(thm)],[])).
% 127.75/82.21 tff(153,plain,
% 127.75/82.21 (^[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)))))),
% 127.75/82.21 inference(bind,[status(th)],[])).
% 127.75/82.21 tff(154,plain,
% 127.75/82.21 (![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)))),
% 127.75/82.21 inference(quant_intro,[status(thm)],[153])).
% 127.75/82.21 tff(155,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')).
% 127.75/82.21 tff(156,plain,
% 127.75/82.21 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 127.75/82.21 inference(modus_ponens,[status(thm)],[155, 154])).
% 127.75/82.21 tff(157,plain,
% 127.75/82.21 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 127.75/82.21 inference(modus_ponens,[status(thm)],[156, 152])).
% 127.75/82.21 tff(158,plain,(
% 127.75/82.21 ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 127.75/82.21 inference(skolemize,[status(sab)],[157])).
% 127.75/82.21 tff(159,plain,
% 127.75/82.21 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 127.75/82.21 inference(modus_ponens,[status(thm)],[158, 151])).
% 127.75/82.21 tff(160,plain,
% 127.75/82.21 (((~![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(d), do(putdown(c, a), do(pickup(c), s0))))) | (~holds(holding(d), do(pickup(d), do(putdown(c, a), do(pickup(c), s0))))) | holds(on(d, c), do(putdown(d, c), do(pickup(d), do(putdown(c, a), 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(d), do(putdown(c, a), do(pickup(c), s0))))) | (~holds(holding(d), do(pickup(d), do(putdown(c, a), do(pickup(c), s0))))) | holds(on(d, c), do(putdown(d, c), do(pickup(d), do(putdown(c, a), do(pickup(c), s0))))))),
% 127.75/82.21 inference(rewrite,[status(thm)],[])).
% 127.75/82.21 tff(161,plain,
% 127.75/82.21 ((~![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(d), do(putdown(c, a), do(pickup(c), s0))))) | (~holds(holding(d), do(pickup(d), do(putdown(c, a), do(pickup(c), s0))))) | holds(on(d, c), do(putdown(d, c), do(pickup(d), do(putdown(c, a), do(pickup(c), s0))))))),
% 127.75/82.21 inference(quant_inst,[status(thm)],[])).
% 127.75/82.21 tff(162,plain,
% 127.75/82.21 ((~![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(d), do(putdown(c, a), do(pickup(c), s0))))) | (~holds(holding(d), do(pickup(d), do(putdown(c, a), do(pickup(c), s0))))) | holds(on(d, c), do(putdown(d, c), do(pickup(d), do(putdown(c, a), do(pickup(c), s0)))))),
% 127.75/82.21 inference(modus_ponens,[status(thm)],[161, 160])).
% 127.75/82.21 tff(163,plain,
% 127.75/82.21 (holds(on(d, c), do(putdown(d, c), do(pickup(d), do(putdown(c, a), do(pickup(c), s0)))))),
% 127.75/82.21 inference(unit_resolution,[status(thm)],[162, 159, 149, 74])).
% 127.75/82.21 tff(164,plain,
% 127.75/82.21 (^[State: $i] : refl((~holds(on(d, c), State)) <=> (~holds(on(d, c), State)))),
% 127.75/82.21 inference(bind,[status(th)],[])).
% 127.75/82.21 tff(165,plain,
% 127.75/82.21 (![State: $i] : (~holds(on(d, c), State)) <=> ![State: $i] : (~holds(on(d, c), State))),
% 127.75/82.21 inference(quant_intro,[status(thm)],[164])).
% 127.75/82.21 tff(166,plain,
% 127.75/82.21 (![State: $i] : (~holds(on(d, c), State)) <=> ![State: $i] : (~holds(on(d, c), State))),
% 127.75/82.21 inference(rewrite,[status(thm)],[])).
% 127.75/82.21 tff(167,axiom,(![State: $i] : (~holds(on(d, c), State))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_DC')).
% 127.75/82.21 tff(168,plain,
% 127.75/82.21 (![State: $i] : (~holds(on(d, c), State))),
% 127.75/82.21 inference(modus_ponens,[status(thm)],[167, 166])).
% 127.75/82.21 tff(169,plain,(
% 127.75/82.21 ![State: $i] : (~holds(on(d, c), State))),
% 127.75/82.21 inference(skolemize,[status(sab)],[168])).
% 127.75/82.21 tff(170,plain,
% 127.75/82.21 (![State: $i] : (~holds(on(d, c), State))),
% 127.75/82.21 inference(modus_ponens,[status(thm)],[169, 165])).
% 127.75/82.21 tff(171,plain,
% 127.75/82.21 ((~![State: $i] : (~holds(on(d, c), State))) | (~holds(on(d, c), do(putdown(d, c), do(pickup(d), do(putdown(c, a), do(pickup(c), s0))))))),
% 127.75/82.21 inference(quant_inst,[status(thm)],[])).
% 127.75/82.21 tff(172,plain,
% 127.75/82.21 ($false),
% 127.75/82.21 inference(unit_resolution,[status(thm)],[171, 170, 163])).
% 127.75/82.21 % SZS output end Proof
%------------------------------------------------------------------------------