%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PLA006-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 : Sat Jun 21 05:22:50 AM UTC 2025
% Result : Unsatisfiable 0.50s 0.69s
% Output : Proof 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PLA006-1 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:19:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.50/0.69 % SZS status Unsatisfiable
% 0.50/0.69 % SZS output start Proof
% 0.50/0.69 tff(holds_type, type, (
% 0.50/0.69 holds: ( $i * $i ) > $o)).
% 0.50/0.69 tff(do_type, type, (
% 0.50/0.69 do: ( $i * $i ) > $i)).
% 0.50/0.69 tff(s0_type, type, (
% 0.50/0.69 s0: $i)).
% 0.50/0.69 tff(pickup_type, type, (
% 0.50/0.69 pickup: $i > $i)).
% 0.50/0.69 tff(c_type, type, (
% 0.50/0.69 c: $i)).
% 0.50/0.69 tff(putdown_type, type, (
% 0.50/0.69 putdown: ( $i * $i ) > $i)).
% 0.50/0.69 tff(table_type, type, (
% 0.50/0.69 table: $i)).
% 0.50/0.69 tff(on_type, type, (
% 0.50/0.69 on: ( $i * $i ) > $i)).
% 0.50/0.69 tff(clear_type, type, (
% 0.50/0.69 clear: $i > $i)).
% 0.50/0.69 tff(differ_type, type, (
% 0.50/0.69 differ: ( $i * $i ) > $o)).
% 0.50/0.69 tff(holding_type, type, (
% 0.50/0.69 holding: $i > $i)).
% 0.50/0.69 tff(empty_type, type, (
% 0.50/0.69 empty: $i)).
% 0.50/0.69 tff(1,assumption,(~holds(clear(table), s0)), introduced(assumption)).
% 0.50/0.69 tff(2,plain,
% 0.50/0.69 (^[State: $i] : refl(holds(clear(table), State) <=> holds(clear(table), State))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(3,plain,
% 0.50/0.69 (![State: $i] : holds(clear(table), State) <=> ![State: $i] : holds(clear(table), State)),
% 0.50/0.69 inference(quant_intro,[status(thm)],[2])).
% 0.50/0.69 tff(4,plain,
% 0.50/0.69 (![State: $i] : holds(clear(table), State) <=> ![State: $i] : holds(clear(table), State)),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(5,axiom,(![State: $i] : holds(clear(table), State)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','clear_table')).
% 0.50/0.69 tff(6,plain,
% 0.50/0.69 (![State: $i] : holds(clear(table), State)),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.50/0.69 tff(7,plain,(
% 0.50/0.69 ![State: $i] : holds(clear(table), State)),
% 0.50/0.69 inference(skolemize,[status(sab)],[6])).
% 0.50/0.69 tff(8,plain,
% 0.50/0.69 (![State: $i] : holds(clear(table), State)),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.50/0.69 tff(9,plain,
% 0.50/0.69 ((~![State: $i] : holds(clear(table), State)) | holds(clear(table), s0)),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(10,plain,
% 0.50/0.69 ($false),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.50/0.69 tff(11,plain,(holds(clear(table), s0)), inference(lemma,lemma(discharge,[]))).
% 0.50/0.69 tff(12,plain,
% 0.50/0.69 (differ(c, table) <=> differ(c, table)),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(13,axiom,(differ(c, table)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','differ_c_table')).
% 0.50/0.69 tff(14,plain,
% 0.50/0.69 (differ(c, table)),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.50/0.69 tff(15,plain,
% 0.50/0.69 (^[Y: $i, X: $i] : refl(((~differ(Y, X)) | differ(X, Y)) <=> ((~differ(Y, X)) | differ(X, Y)))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(16,plain,
% 0.50/0.69 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y)) <=> ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[15])).
% 0.50/0.69 tff(17,plain,
% 0.50/0.69 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y)) <=> ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(18,plain,
% 0.50/0.69 (^[Y: $i, X: $i] : rewrite((differ(X, Y) | (~differ(Y, X))) <=> ((~differ(Y, X)) | differ(X, Y)))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(19,plain,
% 0.50/0.69 (![Y: $i, X: $i] : (differ(X, Y) | (~differ(Y, X))) <=> ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[18])).
% 0.50/0.69 tff(20,axiom,(![Y: $i, X: $i] : (differ(X, Y) | (~differ(Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','symmetry_of_differ')).
% 0.50/0.69 tff(21,plain,
% 0.50/0.69 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.50/0.69 tff(22,plain,
% 0.50/0.69 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.50/0.69 tff(23,plain,(
% 0.50/0.69 ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 0.50/0.69 inference(skolemize,[status(sab)],[22])).
% 0.50/0.69 tff(24,plain,
% 0.50/0.69 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.50/0.69 tff(25,plain,
% 0.50/0.69 (((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | ((~differ(c, table)) | differ(table, c))) <=> ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | (~differ(c, table)) | differ(table, c))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(26,plain,
% 0.50/0.69 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | ((~differ(c, table)) | differ(table, c))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(27,plain,
% 0.50/0.69 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | (~differ(c, table)) | differ(table, c)),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.50/0.69 tff(28,plain,
% 0.50/0.69 (differ(table, c)),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.50/0.69 tff(29,plain,
% 0.50/0.69 (^[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))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(30,plain,
% 0.50/0.69 (![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)))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[29])).
% 0.50/0.69 tff(31,plain,
% 0.50/0.69 (![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)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(32,plain,
% 0.50/0.69 (^[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)))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(33,plain,
% 0.50/0.69 (![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)))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[32])).
% 0.50/0.69 tff(34,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')).
% 0.50/0.69 tff(35,plain,
% 0.50/0.69 (![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.50/0.69 tff(36,plain,
% 0.50/0.69 (![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.50/0.69 tff(37,plain,(
% 0.50/0.69 ![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 0.50/0.69 inference(skolemize,[status(sab)],[36])).
% 0.50/0.69 tff(38,plain,
% 0.50/0.69 (![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.50/0.69 tff(39,plain,
% 0.50/0.69 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(table), s0)) | (~differ(table, c)) | holds(clear(table), do(pickup(c), s0)))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~holds(clear(table), s0)) | (~differ(table, c)) | holds(clear(table), do(pickup(c), s0)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(40,plain,
% 0.50/0.69 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(table), s0)) | (~differ(table, c)) | holds(clear(table), do(pickup(c), s0)))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(41,plain,
% 0.50/0.69 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~holds(clear(table), s0)) | (~differ(table, c)) | holds(clear(table), do(pickup(c), s0))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.50/0.69 tff(42,plain,
% 0.50/0.69 ((~holds(clear(table), s0)) | holds(clear(table), do(pickup(c), s0))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[41, 38, 28])).
% 0.50/0.69 tff(43,plain,
% 0.50/0.69 (holds(clear(table), do(pickup(c), s0))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[42, 11])).
% 0.50/0.69 tff(44,plain,
% 0.50/0.69 (holds(empty, s0) <=> holds(empty, s0)),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(45,axiom,(holds(empty, s0)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','initial_state8')).
% 0.50/0.69 tff(46,plain,
% 0.50/0.69 (holds(empty, s0)),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.50/0.69 tff(47,plain,
% 0.50/0.69 (holds(clear(c), s0) <=> holds(clear(c), s0)),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(48,axiom,(holds(clear(c), s0)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','initial_state7')).
% 0.50/0.69 tff(49,plain,
% 0.50/0.69 (holds(clear(c), s0)),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.50/0.69 tff(50,plain,
% 0.50/0.69 (^[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))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(51,plain,
% 0.50/0.69 (![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)))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[50])).
% 0.50/0.69 tff(52,plain,
% 0.50/0.69 (![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)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(53,plain,
% 0.50/0.69 (^[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)))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(54,plain,
% 0.50/0.69 (![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)))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[53])).
% 0.50/0.69 tff(55,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')).
% 0.50/0.69 tff(56,plain,
% 0.50/0.69 (![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.50/0.69 tff(57,plain,
% 0.50/0.69 (![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.50/0.69 tff(58,plain,(
% 0.50/0.69 ![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 0.50/0.69 inference(skolemize,[status(sab)],[57])).
% 0.50/0.69 tff(59,plain,
% 0.50/0.69 (![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.50/0.69 tff(60,plain,
% 0.50/0.69 (((~![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)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(61,plain,
% 0.50/0.69 (((~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)))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(62,plain,
% 0.50/0.69 (((~![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))))),
% 0.50/0.69 inference(monotonicity,[status(thm)],[61])).
% 0.50/0.69 tff(63,plain,
% 0.50/0.69 (((~![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)))),
% 0.50/0.69 inference(transitivity,[status(thm)],[62, 60])).
% 0.50/0.69 tff(64,plain,
% 0.50/0.69 ((~![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)))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(65,plain,
% 0.50/0.69 ((~![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))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.50/0.69 tff(66,plain,
% 0.50/0.69 (holds(holding(c), do(pickup(c), s0))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[65, 59, 14, 49, 46])).
% 0.50/0.69 tff(67,plain,
% 0.50/0.69 (^[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))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(68,plain,
% 0.50/0.70 (![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)))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[67])).
% 0.50/0.70 tff(69,plain,
% 0.50/0.70 (![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)))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(70,plain,
% 0.50/0.70 (^[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)))))),
% 0.50/0.70 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(71,plain,
% 0.50/0.70 (![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)))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[70])).
% 0.50/0.70 tff(72,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')).
% 0.50/0.70 tff(73,plain,
% 0.50/0.70 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.50/0.70 tff(74,plain,
% 0.50/0.70 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.50/0.70 tff(75,plain,(
% 0.50/0.70 ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 0.50/0.70 inference(skolemize,[status(sab)],[74])).
% 0.50/0.70 tff(76,plain,
% 0.50/0.70 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.50/0.70 tff(77,plain,
% 0.50/0.70 (((~![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(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(on(c, table), do(putdown(c, table), do(pickup(c), s0))))) <=> ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))) | (~holds(clear(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(on(c, table), do(putdown(c, table), do(pickup(c), s0))))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(78,plain,
% 0.50/0.70 ((~![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(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(on(c, table), do(putdown(c, table), do(pickup(c), s0))))),
% 0.50/0.70 inference(quant_inst,[status(thm)],[])).
% 0.50/0.70 tff(79,plain,
% 0.50/0.70 ((~![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(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(on(c, table), do(putdown(c, table), do(pickup(c), s0)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.50/0.70 tff(80,plain,
% 0.50/0.70 (holds(on(c, table), do(putdown(c, table), do(pickup(c), s0)))),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[79, 76, 66, 43])).
% 0.50/0.70 tff(81,plain,
% 0.50/0.70 (^[State: $i] : refl((~holds(on(c, table), State)) <=> (~holds(on(c, table), State)))),
% 0.50/0.70 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(82,plain,
% 0.50/0.70 (![State: $i] : (~holds(on(c, table), State)) <=> ![State: $i] : (~holds(on(c, table), State))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[81])).
% 0.50/0.70 tff(83,plain,
% 0.50/0.70 (![State: $i] : (~holds(on(c, table), State)) <=> ![State: $i] : (~holds(on(c, table), State))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(84,axiom,(![State: $i] : (~holds(on(c, table), State))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_CTable')).
% 0.50/0.70 tff(85,plain,
% 0.50/0.70 (![State: $i] : (~holds(on(c, table), State))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.50/0.70 tff(86,plain,(
% 0.50/0.70 ![State: $i] : (~holds(on(c, table), State))),
% 0.50/0.70 inference(skolemize,[status(sab)],[85])).
% 0.50/0.70 tff(87,plain,
% 0.50/0.70 (![State: $i] : (~holds(on(c, table), State))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.50/0.70 tff(88,plain,
% 0.50/0.70 ((~![State: $i] : (~holds(on(c, table), State))) | (~holds(on(c, table), do(putdown(c, table), do(pickup(c), s0))))),
% 0.50/0.70 inference(quant_inst,[status(thm)],[])).
% 0.50/0.70 tff(89,plain,
% 0.50/0.70 ($false),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[88, 87, 80])).
% 0.50/0.70 % SZS output end Proof
% 0.50/0.70 % E exiting
%------------------------------------------------------------------------------