%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PLA019-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:22:51 AM UTC 2025
% Result : Unsatisfiable 10.56s 10.73s
% Output : Proof 10.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : PLA019-1 : TPTP v9.0.0. Released v1.1.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n001.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 02:25:34 EDT 2025
% 0.11/0.33 % CPUTime :
% 10.56/10.73 % SZS status Unsatisfiable
% 10.56/10.73 % SZS output start Proof
% 10.56/10.73 tff(holds_type, type, (
% 10.56/10.73 holds: ( $i * $i ) > $o)).
% 10.56/10.73 tff(do_type, type, (
% 10.56/10.73 do: ( $i * $i ) > $i)).
% 10.56/10.73 tff(s0_type, type, (
% 10.56/10.73 s0: $i)).
% 10.56/10.73 tff(pickup_type, type, (
% 10.56/10.73 pickup: $i > $i)).
% 10.56/10.73 tff(c_type, type, (
% 10.56/10.73 c: $i)).
% 10.56/10.73 tff(putdown_type, type, (
% 10.56/10.73 putdown: ( $i * $i ) > $i)).
% 10.56/10.73 tff(table_type, type, (
% 10.56/10.73 table: $i)).
% 10.56/10.73 tff(d_type, type, (
% 10.56/10.73 d: $i)).
% 10.56/10.73 tff(on_type, type, (
% 10.56/10.73 on: ( $i * $i ) > $i)).
% 10.56/10.73 tff(clear_type, type, (
% 10.56/10.73 clear: $i > $i)).
% 10.56/10.73 tff(holding_type, type, (
% 10.56/10.73 holding: $i > $i)).
% 10.56/10.73 tff(differ_type, type, (
% 10.56/10.73 differ: ( $i * $i ) > $o)).
% 10.56/10.73 tff(empty_type, type, (
% 10.56/10.73 empty: $i)).
% 10.56/10.73 tff(1,assumption,(~holds(clear(table), s0)), introduced(assumption)).
% 10.56/10.73 tff(2,plain,
% 10.56/10.73 (^[State: $i] : refl(holds(clear(table), State) <=> holds(clear(table), State))),
% 10.56/10.73 inference(bind,[status(th)],[])).
% 10.56/10.73 tff(3,plain,
% 10.56/10.73 (![State: $i] : holds(clear(table), State) <=> ![State: $i] : holds(clear(table), State)),
% 10.56/10.73 inference(quant_intro,[status(thm)],[2])).
% 10.56/10.73 tff(4,plain,
% 10.56/10.73 (![State: $i] : holds(clear(table), State) <=> ![State: $i] : holds(clear(table), State)),
% 10.56/10.73 inference(rewrite,[status(thm)],[])).
% 10.56/10.73 tff(5,axiom,(![State: $i] : holds(clear(table), State)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','clear_table')).
% 10.56/10.73 tff(6,plain,
% 10.56/10.73 (![State: $i] : holds(clear(table), State)),
% 10.56/10.73 inference(modus_ponens,[status(thm)],[5, 4])).
% 10.56/10.73 tff(7,plain,(
% 10.56/10.73 ![State: $i] : holds(clear(table), State)),
% 10.56/10.73 inference(skolemize,[status(sab)],[6])).
% 10.56/10.73 tff(8,plain,
% 10.56/10.73 (![State: $i] : holds(clear(table), State)),
% 10.56/10.73 inference(modus_ponens,[status(thm)],[7, 3])).
% 10.56/10.73 tff(9,plain,
% 10.56/10.73 ((~![State: $i] : holds(clear(table), State)) | holds(clear(table), s0)),
% 10.56/10.73 inference(quant_inst,[status(thm)],[])).
% 10.56/10.73 tff(10,plain,
% 10.56/10.73 ($false),
% 10.56/10.73 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 10.56/10.73 tff(11,plain,(holds(clear(table), s0)), inference(lemma,lemma(discharge,[]))).
% 10.56/10.73 tff(12,plain,
% 10.56/10.73 (differ(c, table) <=> differ(c, table)),
% 10.56/10.73 inference(rewrite,[status(thm)],[])).
% 10.56/10.73 tff(13,axiom,(differ(c, table)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','differ_c_table')).
% 10.56/10.73 tff(14,plain,
% 10.56/10.73 (differ(c, table)),
% 10.56/10.73 inference(modus_ponens,[status(thm)],[13, 12])).
% 10.56/10.73 tff(15,plain,
% 10.56/10.73 (^[Y: $i, X: $i] : refl(((~differ(Y, X)) | differ(X, Y)) <=> ((~differ(Y, X)) | differ(X, Y)))),
% 10.56/10.73 inference(bind,[status(th)],[])).
% 10.56/10.73 tff(16,plain,
% 10.56/10.73 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y)) <=> ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 10.56/10.73 inference(quant_intro,[status(thm)],[15])).
% 10.56/10.73 tff(17,plain,
% 10.56/10.73 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y)) <=> ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 10.56/10.73 inference(rewrite,[status(thm)],[])).
% 10.56/10.73 tff(18,plain,
% 10.56/10.73 (^[Y: $i, X: $i] : rewrite((differ(X, Y) | (~differ(Y, X))) <=> ((~differ(Y, X)) | differ(X, Y)))),
% 10.56/10.73 inference(bind,[status(th)],[])).
% 10.56/10.73 tff(19,plain,
% 10.56/10.73 (![Y: $i, X: $i] : (differ(X, Y) | (~differ(Y, X))) <=> ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 10.56/10.73 inference(quant_intro,[status(thm)],[18])).
% 10.56/10.73 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')).
% 10.56/10.73 tff(21,plain,
% 10.56/10.73 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 10.56/10.73 inference(modus_ponens,[status(thm)],[20, 19])).
% 10.56/10.73 tff(22,plain,
% 10.56/10.73 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 10.56/10.73 inference(modus_ponens,[status(thm)],[21, 17])).
% 10.56/10.73 tff(23,plain,(
% 10.56/10.73 ![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 10.56/10.73 inference(skolemize,[status(sab)],[22])).
% 10.56/10.73 tff(24,plain,
% 10.56/10.73 (![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))),
% 10.56/10.73 inference(modus_ponens,[status(thm)],[23, 16])).
% 10.56/10.73 tff(25,plain,
% 10.56/10.73 (((~![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))),
% 10.56/10.73 inference(rewrite,[status(thm)],[])).
% 10.56/10.73 tff(26,plain,
% 10.56/10.73 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | ((~differ(c, table)) | differ(table, c))),
% 10.56/10.73 inference(quant_inst,[status(thm)],[])).
% 10.56/10.73 tff(27,plain,
% 10.56/10.73 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | (~differ(c, table)) | differ(table, c)),
% 10.56/10.73 inference(modus_ponens,[status(thm)],[26, 25])).
% 10.56/10.73 tff(28,plain,
% 10.56/10.73 (differ(table, c)),
% 10.56/10.73 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 10.56/10.73 tff(29,plain,
% 10.56/10.73 (^[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))))),
% 10.56/10.73 inference(bind,[status(th)],[])).
% 10.56/10.73 tff(30,plain,
% 10.56/10.73 (![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)))),
% 10.56/10.73 inference(quant_intro,[status(thm)],[29])).
% 10.56/10.73 tff(31,plain,
% 10.56/10.73 (![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)))),
% 10.56/10.73 inference(rewrite,[status(thm)],[])).
% 10.56/10.73 tff(32,plain,
% 10.56/10.73 (^[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)))))),
% 10.56/10.73 inference(bind,[status(th)],[])).
% 10.56/10.73 tff(33,plain,
% 10.56/10.73 (![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)))),
% 10.56/10.73 inference(quant_intro,[status(thm)],[32])).
% 10.56/10.73 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')).
% 10.56/10.73 tff(35,plain,
% 10.56/10.73 (![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 10.56/10.73 inference(modus_ponens,[status(thm)],[34, 33])).
% 10.56/10.73 tff(36,plain,
% 10.56/10.73 (![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 10.56/10.73 inference(modus_ponens,[status(thm)],[35, 31])).
% 10.56/10.73 tff(37,plain,(
% 10.56/10.73 ![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 10.56/10.73 inference(skolemize,[status(sab)],[36])).
% 10.56/10.73 tff(38,plain,
% 10.56/10.73 (![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))),
% 10.56/10.73 inference(modus_ponens,[status(thm)],[37, 30])).
% 10.56/10.73 tff(39,plain,
% 10.56/10.73 (((~![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)))),
% 10.56/10.73 inference(rewrite,[status(thm)],[])).
% 10.56/10.73 tff(40,plain,
% 10.56/10.73 ((~![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)))),
% 10.56/10.73 inference(quant_inst,[status(thm)],[])).
% 10.56/10.73 tff(41,plain,
% 10.56/10.73 ((~![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))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[40, 39])).
% 10.56/10.74 tff(42,plain,
% 10.56/10.74 ((~holds(clear(table), s0)) | holds(clear(table), do(pickup(c), s0))),
% 10.56/10.74 inference(unit_resolution,[status(thm)],[41, 38, 28])).
% 10.56/10.74 tff(43,plain,
% 10.56/10.74 (holds(clear(table), do(pickup(c), s0))),
% 10.56/10.74 inference(unit_resolution,[status(thm)],[42, 11])).
% 10.56/10.74 tff(44,plain,
% 10.56/10.74 (holds(empty, s0) <=> holds(empty, s0)),
% 10.56/10.74 inference(rewrite,[status(thm)],[])).
% 10.56/10.74 tff(45,axiom,(holds(empty, s0)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','initial_state8')).
% 10.56/10.74 tff(46,plain,
% 10.56/10.74 (holds(empty, s0)),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[45, 44])).
% 10.56/10.74 tff(47,plain,
% 10.56/10.74 (holds(clear(c), s0) <=> holds(clear(c), s0)),
% 10.56/10.74 inference(rewrite,[status(thm)],[])).
% 10.56/10.74 tff(48,axiom,(holds(clear(c), s0)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','initial_state7')).
% 10.56/10.74 tff(49,plain,
% 10.56/10.74 (holds(clear(c), s0)),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[48, 47])).
% 10.56/10.74 tff(50,plain,
% 10.56/10.74 (^[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))))),
% 10.56/10.74 inference(bind,[status(th)],[])).
% 10.56/10.74 tff(51,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(quant_intro,[status(thm)],[50])).
% 10.56/10.74 tff(52,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(rewrite,[status(thm)],[])).
% 10.56/10.74 tff(53,plain,
% 10.56/10.74 (^[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)))))),
% 10.56/10.74 inference(bind,[status(th)],[])).
% 10.56/10.74 tff(54,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(quant_intro,[status(thm)],[53])).
% 10.56/10.74 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')).
% 10.56/10.74 tff(56,plain,
% 10.56/10.74 (![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[55, 54])).
% 10.56/10.74 tff(57,plain,
% 10.56/10.74 (![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[56, 52])).
% 10.56/10.74 tff(58,plain,(
% 10.56/10.74 ![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 10.56/10.74 inference(skolemize,[status(sab)],[57])).
% 10.56/10.74 tff(59,plain,
% 10.56/10.74 (![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[58, 51])).
% 10.56/10.74 tff(60,plain,
% 10.56/10.74 (((~![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)))),
% 10.56/10.74 inference(rewrite,[status(thm)],[])).
% 10.56/10.74 tff(61,plain,
% 10.56/10.74 (((~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)))),
% 10.56/10.74 inference(rewrite,[status(thm)],[])).
% 10.56/10.74 tff(62,plain,
% 10.56/10.74 (((~![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))))),
% 10.56/10.74 inference(monotonicity,[status(thm)],[61])).
% 10.56/10.74 tff(63,plain,
% 10.56/10.74 (((~![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)))),
% 10.56/10.74 inference(transitivity,[status(thm)],[62, 60])).
% 10.56/10.74 tff(64,plain,
% 10.56/10.74 ((~![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)))),
% 10.56/10.74 inference(quant_inst,[status(thm)],[])).
% 10.56/10.74 tff(65,plain,
% 10.56/10.74 ((~![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))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[64, 63])).
% 10.56/10.74 tff(66,plain,
% 10.56/10.74 (holds(holding(c), do(pickup(c), s0))),
% 10.56/10.74 inference(unit_resolution,[status(thm)],[65, 59, 14, 49, 46])).
% 10.56/10.74 tff(67,plain,
% 10.56/10.74 (^[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))))),
% 10.56/10.74 inference(bind,[status(th)],[])).
% 10.56/10.74 tff(68,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(quant_intro,[status(thm)],[67])).
% 10.56/10.74 tff(69,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(rewrite,[status(thm)],[])).
% 10.56/10.74 tff(70,plain,
% 10.56/10.74 (^[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)))))),
% 10.56/10.74 inference(bind,[status(th)],[])).
% 10.56/10.74 tff(71,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(quant_intro,[status(thm)],[70])).
% 10.56/10.74 tff(72,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')).
% 10.56/10.74 tff(73,plain,
% 10.56/10.74 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[72, 71])).
% 10.56/10.74 tff(74,plain,
% 10.56/10.74 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[73, 69])).
% 10.56/10.74 tff(75,plain,(
% 10.56/10.74 ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 10.56/10.74 inference(skolemize,[status(sab)],[74])).
% 10.56/10.74 tff(76,plain,
% 10.56/10.74 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[75, 68])).
% 10.56/10.74 tff(77,plain,
% 10.56/10.74 (((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | ((~holds(clear(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(clear(c), do(putdown(c, table), do(pickup(c), s0))))) <=> ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | (~holds(clear(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(clear(c), do(putdown(c, table), do(pickup(c), s0))))),
% 10.56/10.74 inference(rewrite,[status(thm)],[])).
% 10.56/10.74 tff(78,plain,
% 10.56/10.74 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | ((~holds(clear(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(clear(c), do(putdown(c, table), do(pickup(c), s0))))),
% 10.56/10.74 inference(quant_inst,[status(thm)],[])).
% 10.56/10.74 tff(79,plain,
% 10.56/10.74 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | (~holds(clear(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(clear(c), do(putdown(c, table), do(pickup(c), s0)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[78, 77])).
% 10.56/10.74 tff(80,plain,
% 10.56/10.74 (holds(clear(c), do(putdown(c, table), do(pickup(c), s0)))),
% 10.56/10.74 inference(unit_resolution,[status(thm)],[79, 76, 66, 43])).
% 10.56/10.74 tff(81,plain,
% 10.56/10.74 (^[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))))),
% 10.56/10.74 inference(bind,[status(th)],[])).
% 10.56/10.74 tff(82,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(quant_intro,[status(thm)],[81])).
% 10.56/10.74 tff(83,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(rewrite,[status(thm)],[])).
% 10.56/10.74 tff(84,plain,
% 10.56/10.74 (^[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)))))),
% 10.56/10.74 inference(bind,[status(th)],[])).
% 10.56/10.74 tff(85,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(quant_intro,[status(thm)],[84])).
% 10.56/10.74 tff(86,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')).
% 10.56/10.74 tff(87,plain,
% 10.56/10.74 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[86, 85])).
% 10.56/10.74 tff(88,plain,
% 10.56/10.74 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[87, 83])).
% 10.56/10.74 tff(89,plain,(
% 10.56/10.74 ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 10.56/10.74 inference(skolemize,[status(sab)],[88])).
% 10.56/10.74 tff(90,plain,
% 10.56/10.74 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[89, 82])).
% 10.56/10.74 tff(91,plain,
% 10.56/10.74 (((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | ((~holds(clear(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(empty, do(putdown(c, table), do(pickup(c), s0))))) <=> ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | (~holds(clear(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(empty, do(putdown(c, table), do(pickup(c), s0))))),
% 10.56/10.74 inference(rewrite,[status(thm)],[])).
% 10.56/10.74 tff(92,plain,
% 10.56/10.74 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | ((~holds(clear(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(empty, do(putdown(c, table), do(pickup(c), s0))))),
% 10.56/10.74 inference(quant_inst,[status(thm)],[])).
% 10.56/10.74 tff(93,plain,
% 10.56/10.74 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | (~holds(clear(table), do(pickup(c), s0))) | (~holds(holding(c), do(pickup(c), s0))) | holds(empty, do(putdown(c, table), do(pickup(c), s0)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[92, 91])).
% 10.56/10.74 tff(94,plain,
% 10.56/10.74 (holds(empty, do(putdown(c, table), do(pickup(c), s0)))),
% 10.56/10.74 inference(unit_resolution,[status(thm)],[93, 90, 66, 43])).
% 10.56/10.74 tff(95,plain,
% 10.56/10.74 (((~![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), do(putdown(c, table), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | holds(holding(c), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) <=> ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | (~differ(c, table)) | (~holds(clear(c), do(putdown(c, table), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | holds(holding(c), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))),
% 10.56/10.74 inference(rewrite,[status(thm)],[])).
% 10.56/10.74 tff(96,plain,
% 10.56/10.74 ((~![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), do(putdown(c, table), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | holds(holding(c), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))),
% 10.56/10.74 inference(quant_inst,[status(thm)],[])).
% 10.56/10.74 tff(97,plain,
% 10.56/10.74 ((~![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), do(putdown(c, table), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | holds(holding(c), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[96, 95])).
% 10.56/10.74 tff(98,plain,
% 10.56/10.74 (holds(holding(c), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))),
% 10.56/10.74 inference(unit_resolution,[status(thm)],[97, 59, 14, 94, 80])).
% 10.56/10.74 tff(99,plain,
% 10.56/10.74 (^[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))))),
% 10.56/10.74 inference(bind,[status(th)],[])).
% 10.56/10.74 tff(100,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(quant_intro,[status(thm)],[99])).
% 10.56/10.74 tff(101,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(rewrite,[status(thm)],[])).
% 10.56/10.74 tff(102,plain,
% 10.56/10.74 (^[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)))))),
% 10.56/10.74 inference(bind,[status(th)],[])).
% 10.56/10.74 tff(103,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(quant_intro,[status(thm)],[102])).
% 10.56/10.74 tff(104,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')).
% 10.56/10.74 tff(105,plain,
% 10.56/10.74 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[104, 103])).
% 10.56/10.74 tff(106,plain,
% 10.56/10.74 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[105, 101])).
% 10.56/10.74 tff(107,plain,(
% 10.56/10.74 ![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 10.56/10.74 inference(skolemize,[status(sab)],[106])).
% 10.56/10.74 tff(108,plain,
% 10.56/10.74 (![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(on(X, Y), do(putdown(X, Y), State)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[107, 100])).
% 10.56/10.74 tff(109,plain,
% 10.56/10.74 (((~![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))))),
% 10.56/10.74 inference(rewrite,[status(thm)],[])).
% 10.56/10.74 tff(110,plain,
% 10.56/10.74 ((~![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))))),
% 10.56/10.74 inference(quant_inst,[status(thm)],[])).
% 10.56/10.74 tff(111,plain,
% 10.56/10.74 ((~![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)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[110, 109])).
% 10.56/10.74 tff(112,plain,
% 10.56/10.74 (holds(on(c, table), do(putdown(c, table), do(pickup(c), s0)))),
% 10.56/10.74 inference(unit_resolution,[status(thm)],[111, 108, 66, 43])).
% 10.56/10.74 tff(113,plain,
% 10.56/10.74 (^[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))))),
% 10.56/10.74 inference(bind,[status(th)],[])).
% 10.56/10.74 tff(114,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(quant_intro,[status(thm)],[113])).
% 10.56/10.74 tff(115,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(rewrite,[status(thm)],[])).
% 10.56/10.74 tff(116,plain,
% 10.56/10.74 (^[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)))))),
% 10.56/10.74 inference(bind,[status(th)],[])).
% 10.56/10.74 tff(117,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(quant_intro,[status(thm)],[116])).
% 10.56/10.74 tff(118,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')).
% 10.56/10.74 tff(119,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[118, 117])).
% 10.56/10.74 tff(120,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[119, 115])).
% 10.56/10.74 tff(121,plain,(
% 10.56/10.74 ![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)))),
% 10.56/10.74 inference(skolemize,[status(sab)],[120])).
% 10.56/10.74 tff(122,plain,
% 10.56/10.74 (![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)))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[121, 114])).
% 10.56/10.74 tff(123,plain,
% 10.56/10.74 (((~![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), do(putdown(c, table), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | (~holds(on(c, table), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(table), do(pickup(c), do(putdown(c, table), 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(clear(c), do(putdown(c, table), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | (~holds(on(c, table), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))),
% 10.56/10.74 inference(rewrite,[status(thm)],[])).
% 10.56/10.74 tff(124,plain,
% 10.56/10.74 ((~![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), do(putdown(c, table), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | (~holds(on(c, table), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))),
% 10.56/10.74 inference(quant_inst,[status(thm)],[])).
% 10.56/10.74 tff(125,plain,
% 10.56/10.74 ((~![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), do(putdown(c, table), do(pickup(c), s0)))) | (~holds(empty, do(putdown(c, table), do(pickup(c), s0)))) | (~holds(on(c, table), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[124, 123])).
% 10.56/10.74 tff(126,plain,
% 10.56/10.74 ((~holds(clear(c), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))),
% 10.56/10.74 inference(unit_resolution,[status(thm)],[125, 122, 94, 112])).
% 10.56/10.74 tff(127,plain,
% 10.56/10.74 (holds(clear(table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))),
% 10.56/10.74 inference(unit_resolution,[status(thm)],[126, 80])).
% 10.56/10.74 tff(128,plain,
% 10.56/10.74 (((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | ((~holds(clear(table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | (~holds(holding(c), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | holds(clear(c), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))) <=> ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | (~holds(clear(table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | (~holds(holding(c), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | holds(clear(c), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))),
% 10.56/10.74 inference(rewrite,[status(thm)],[])).
% 10.56/10.74 tff(129,plain,
% 10.56/10.74 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | ((~holds(clear(table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | (~holds(holding(c), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | holds(clear(c), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))),
% 10.56/10.74 inference(quant_inst,[status(thm)],[])).
% 10.56/10.74 tff(130,plain,
% 10.56/10.74 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(clear(X), do(putdown(X, Y), State)))) | (~holds(clear(table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | (~holds(holding(c), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | holds(clear(c), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[129, 128])).
% 10.56/10.74 tff(131,plain,
% 10.56/10.74 (holds(clear(c), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))),
% 10.56/10.74 inference(unit_resolution,[status(thm)],[130, 76, 127, 98])).
% 10.56/10.74 tff(132,plain,
% 10.56/10.74 (differ(c, d) <=> differ(c, d)),
% 10.56/10.74 inference(rewrite,[status(thm)],[])).
% 10.56/10.74 tff(133,axiom,(differ(c, d)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','differ_c_d')).
% 10.56/10.74 tff(134,plain,
% 10.56/10.74 (differ(c, d)),
% 10.56/10.74 inference(modus_ponens,[status(thm)],[133, 132])).
% 10.56/10.75 tff(135,plain,
% 10.56/10.75 (((~![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, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | holds(clear(c), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~differ(c, d)) | (~holds(clear(c), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | holds(clear(c), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))))),
% 10.56/10.75 inference(rewrite,[status(thm)],[])).
% 10.56/10.75 tff(136,plain,
% 10.56/10.75 (((~holds(clear(c), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~differ(c, d)) | holds(clear(c), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))) <=> ((~differ(c, d)) | (~holds(clear(c), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | holds(clear(c), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))))),
% 10.56/10.75 inference(rewrite,[status(thm)],[])).
% 10.56/10.75 tff(137,plain,
% 10.56/10.75 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(c), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~differ(c, d)) | holds(clear(c), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~differ(c, d)) | (~holds(clear(c), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | holds(clear(c), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))))),
% 10.56/10.75 inference(monotonicity,[status(thm)],[136])).
% 10.56/10.75 tff(138,plain,
% 10.56/10.75 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(c), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~differ(c, d)) | holds(clear(c), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~differ(c, d)) | (~holds(clear(c), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | holds(clear(c), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))))),
% 10.56/10.75 inference(transitivity,[status(thm)],[137, 135])).
% 10.56/10.75 tff(139,plain,
% 10.56/10.75 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(c), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~differ(c, d)) | holds(clear(c), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))))),
% 10.56/10.75 inference(quant_inst,[status(thm)],[])).
% 10.56/10.75 tff(140,plain,
% 10.56/10.75 ((~![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, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | holds(clear(c), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))),
% 10.56/10.75 inference(modus_ponens,[status(thm)],[139, 138])).
% 10.56/10.75 tff(141,plain,
% 10.56/10.75 (holds(clear(c), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))),
% 10.56/10.75 inference(unit_resolution,[status(thm)],[140, 38, 134, 131])).
% 10.56/10.75 tff(142,plain,
% 10.56/10.75 (holds(on(c, d), s0) <=> holds(on(c, d), s0)),
% 10.56/10.75 inference(rewrite,[status(thm)],[])).
% 10.56/10.75 tff(143,axiom,(holds(on(c, d), s0)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','initial_state3')).
% 10.56/10.75 tff(144,plain,
% 10.56/10.75 (holds(on(c, d), s0)),
% 10.56/10.75 inference(modus_ponens,[status(thm)],[143, 142])).
% 10.56/10.75 tff(145,plain,
% 10.56/10.75 (((~![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)))),
% 10.56/10.75 inference(rewrite,[status(thm)],[])).
% 10.56/10.75 tff(146,plain,
% 10.56/10.75 (((~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)))),
% 10.56/10.75 inference(rewrite,[status(thm)],[])).
% 10.56/10.75 tff(147,plain,
% 10.56/10.75 (((~![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))))),
% 10.56/10.75 inference(monotonicity,[status(thm)],[146])).
% 10.56/10.75 tff(148,plain,
% 10.56/10.75 (((~![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)))),
% 10.56/10.75 inference(transitivity,[status(thm)],[147, 145])).
% 10.56/10.75 tff(149,plain,
% 10.56/10.75 ((~![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)))),
% 10.56/10.75 inference(quant_inst,[status(thm)],[])).
% 10.56/10.75 tff(150,plain,
% 10.56/10.75 ((~![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))),
% 10.56/10.75 inference(modus_ponens,[status(thm)],[149, 148])).
% 10.56/10.75 tff(151,plain,
% 10.56/10.75 (holds(clear(d), do(pickup(c), s0))),
% 10.56/10.75 inference(unit_resolution,[status(thm)],[150, 122, 144, 49, 46])).
% 10.56/10.75 tff(152,plain,
% 10.56/10.75 (differ(d, table) <=> differ(d, table)),
% 10.56/10.75 inference(rewrite,[status(thm)],[])).
% 10.56/10.75 tff(153,axiom,(differ(d, table)), file('/export/starexec/sandbox2/benchmark/Axioms/PLA001-1.ax','differ_d_table')).
% 10.56/10.75 tff(154,plain,
% 10.56/10.75 (differ(d, table)),
% 10.56/10.75 inference(modus_ponens,[status(thm)],[153, 152])).
% 10.56/10.75 tff(155,plain,
% 10.56/10.75 (^[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))))),
% 10.56/10.75 inference(bind,[status(th)],[])).
% 10.56/10.75 tff(156,plain,
% 10.56/10.75 (![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)))),
% 10.56/10.75 inference(quant_intro,[status(thm)],[155])).
% 10.56/10.75 tff(157,plain,
% 10.56/10.75 (![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)))),
% 10.56/10.75 inference(rewrite,[status(thm)],[])).
% 10.56/10.75 tff(158,plain,
% 10.56/10.75 (^[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)))))),
% 10.56/10.75 inference(bind,[status(th)],[])).
% 10.56/10.75 tff(159,plain,
% 10.56/10.75 (![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)))),
% 10.56/10.75 inference(quant_intro,[status(thm)],[158])).
% 10.56/10.75 tff(160,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')).
% 10.56/10.75 tff(161,plain,
% 10.56/10.75 (![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 10.56/10.75 inference(modus_ponens,[status(thm)],[160, 159])).
% 10.56/10.75 tff(162,plain,
% 10.56/10.75 (![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 10.56/10.75 inference(modus_ponens,[status(thm)],[161, 157])).
% 10.56/10.75 tff(163,plain,(
% 10.56/10.75 ![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 10.56/10.75 inference(skolemize,[status(sab)],[162])).
% 10.56/10.75 tff(164,plain,
% 10.56/10.75 (![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))),
% 10.56/10.75 inference(modus_ponens,[status(thm)],[163, 156])).
% 10.56/10.75 tff(165,plain,
% 10.56/10.75 (((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | ((~differ(d, table)) | (~holds(clear(d), do(pickup(c), s0))) | holds(clear(d), do(putdown(c, table), do(pickup(c), s0))))) <=> ((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | (~differ(d, table)) | (~holds(clear(d), do(pickup(c), s0))) | holds(clear(d), do(putdown(c, table), do(pickup(c), s0))))),
% 10.56/10.75 inference(rewrite,[status(thm)],[])).
% 10.56/10.75 tff(166,plain,
% 10.56/10.75 ((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | ((~differ(d, table)) | (~holds(clear(d), do(pickup(c), s0))) | holds(clear(d), do(putdown(c, table), do(pickup(c), s0))))),
% 10.56/10.75 inference(quant_inst,[status(thm)],[])).
% 10.56/10.75 tff(167,plain,
% 10.56/10.75 ((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | (~differ(d, table)) | (~holds(clear(d), do(pickup(c), s0))) | holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))),
% 10.56/10.75 inference(modus_ponens,[status(thm)],[166, 165])).
% 10.56/10.75 tff(168,plain,
% 10.56/10.75 (holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))),
% 10.56/10.75 inference(unit_resolution,[status(thm)],[167, 164, 154, 151])).
% 10.56/10.75 tff(169,plain,
% 10.56/10.75 (((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | ((~differ(c, d)) | differ(d, c))) <=> ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | (~differ(c, d)) | differ(d, c))),
% 10.56/10.75 inference(rewrite,[status(thm)],[])).
% 10.56/10.75 tff(170,plain,
% 10.56/10.75 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | ((~differ(c, d)) | differ(d, c))),
% 10.56/10.75 inference(quant_inst,[status(thm)],[])).
% 10.56/10.75 tff(171,plain,
% 10.56/10.75 ((~![Y: $i, X: $i] : ((~differ(Y, X)) | differ(X, Y))) | (~differ(c, d)) | differ(d, c)),
% 10.56/10.75 inference(modus_ponens,[status(thm)],[170, 169])).
% 10.56/10.75 tff(172,plain,
% 10.56/10.75 (differ(d, c)),
% 10.56/10.75 inference(unit_resolution,[status(thm)],[171, 24, 134])).
% 10.56/10.75 tff(173,plain,
% 10.56/10.75 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~differ(d, c)) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(d), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~differ(d, c)) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(d), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))),
% 10.56/10.75 inference(rewrite,[status(thm)],[])).
% 10.56/10.75 tff(174,plain,
% 10.56/10.75 (((~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(d, c)) | holds(clear(d), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) <=> ((~differ(d, c)) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(d), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))),
% 10.56/10.75 inference(rewrite,[status(thm)],[])).
% 10.56/10.75 tff(175,plain,
% 10.56/10.75 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(d, c)) | holds(clear(d), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~differ(d, c)) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(d), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))),
% 10.56/10.75 inference(monotonicity,[status(thm)],[174])).
% 10.56/10.75 tff(176,plain,
% 10.56/10.75 (((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(d, c)) | holds(clear(d), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) <=> ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~differ(d, c)) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(d), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))),
% 10.56/10.75 inference(transitivity,[status(thm)],[175, 173])).
% 10.56/10.75 tff(177,plain,
% 10.56/10.75 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | ((~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | (~differ(d, c)) | holds(clear(d), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))),
% 10.56/10.75 inference(quant_inst,[status(thm)],[])).
% 10.56/10.75 tff(178,plain,
% 10.56/10.75 ((~![Z: $i, State: $i, X: $i] : ((~holds(clear(X), State)) | (~differ(X, Z)) | holds(clear(X), do(pickup(Z), State)))) | (~differ(d, c)) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), s0)))) | holds(clear(d), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))),
% 10.56/10.75 inference(modus_ponens,[status(thm)],[177, 176])).
% 10.56/10.75 tff(179,plain,
% 10.56/10.75 (holds(clear(d), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))),
% 10.56/10.75 inference(unit_resolution,[status(thm)],[178, 38, 172, 168])).
% 10.56/10.75 tff(180,plain,
% 10.56/10.75 (((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | ((~differ(d, table)) | (~holds(clear(d), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | holds(clear(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))) <=> ((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | (~differ(d, table)) | (~holds(clear(d), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | holds(clear(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))),
% 10.56/10.75 inference(rewrite,[status(thm)],[])).
% 10.56/10.75 tff(181,plain,
% 10.56/10.75 ((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | ((~differ(d, table)) | (~holds(clear(d), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | holds(clear(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))),
% 10.56/10.75 inference(quant_inst,[status(thm)],[])).
% 10.56/10.75 tff(182,plain,
% 10.56/10.75 ((~![Z: $i, Y: $i, State: $i, X: $i] : ((~differ(Z, Y)) | (~holds(clear(Z), State)) | holds(clear(Z), do(putdown(X, Y), State)))) | (~differ(d, table)) | (~holds(clear(d), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | holds(clear(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))),
% 10.56/10.75 inference(modus_ponens,[status(thm)],[181, 180])).
% 10.56/10.75 tff(183,plain,
% 10.56/10.75 (holds(clear(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))),
% 10.56/10.75 inference(unit_resolution,[status(thm)],[182, 164, 154, 179])).
% 10.56/10.75 tff(184,plain,
% 10.56/10.75 (((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | ((~holds(clear(table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | (~holds(holding(c), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | holds(empty, do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))) <=> ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | (~holds(clear(table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | (~holds(holding(c), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | holds(empty, do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))),
% 10.56/10.75 inference(rewrite,[status(thm)],[])).
% 10.56/10.75 tff(185,plain,
% 10.56/10.75 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | ((~holds(clear(table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | (~holds(holding(c), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | holds(empty, do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))),
% 10.56/10.75 inference(quant_inst,[status(thm)],[])).
% 10.56/10.75 tff(186,plain,
% 10.56/10.75 ((~![Y: $i, State: $i, X: $i] : ((~holds(clear(Y), State)) | (~holds(holding(X), State)) | holds(empty, do(putdown(X, Y), State)))) | (~holds(clear(table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | (~holds(holding(c), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))) | holds(empty, do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))),
% 10.56/10.75 inference(modus_ponens,[status(thm)],[185, 184])).
% 10.56/10.75 tff(187,plain,
% 10.56/10.75 (holds(empty, do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))),
% 10.56/10.75 inference(unit_resolution,[status(thm)],[186, 90, 127, 98])).
% 10.56/10.75 tff(188,plain,
% 10.56/10.75 (((~![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(holding(d), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(empty, do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))))) <=> ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | (~differ(d, table)) | holds(holding(d), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(empty, do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))))),
% 10.56/10.75 inference(rewrite,[status(thm)],[])).
% 10.56/10.75 tff(189,plain,
% 10.56/10.76 (((~differ(d, table)) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(empty, do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | holds(holding(d), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))) <=> ((~differ(d, table)) | holds(holding(d), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(empty, do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))))),
% 10.56/10.76 inference(rewrite,[status(thm)],[])).
% 10.56/10.76 tff(190,plain,
% 10.56/10.76 (((~![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, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(empty, do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | holds(holding(d), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))))) <=> ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | ((~differ(d, table)) | holds(holding(d), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(empty, do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))))),
% 10.56/10.76 inference(monotonicity,[status(thm)],[189])).
% 10.56/10.76 tff(191,plain,
% 10.56/10.76 (((~![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, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(empty, do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | holds(holding(d), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))))) <=> ((~![State: $i, X: $i] : ((~differ(X, table)) | (~holds(clear(X), State)) | (~holds(empty, State)) | holds(holding(X), do(pickup(X), State)))) | (~differ(d, table)) | holds(holding(d), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(empty, do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))))),
% 10.56/10.76 inference(transitivity,[status(thm)],[190, 188])).
% 10.56/10.76 tff(192,plain,
% 10.56/10.76 ((~![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, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(empty, do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | holds(holding(d), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))))),
% 10.56/10.76 inference(quant_inst,[status(thm)],[])).
% 10.56/10.76 tff(193,plain,
% 10.56/10.76 ((~![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(holding(d), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(clear(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))) | (~holds(empty, do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))),
% 10.56/10.76 inference(modus_ponens,[status(thm)],[192, 191])).
% 10.56/10.76 tff(194,plain,
% 10.56/10.76 (holds(holding(d), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))),
% 10.56/10.76 inference(unit_resolution,[status(thm)],[193, 59, 154, 187, 183])).
% 10.56/10.76 tff(195,plain,
% 10.56/10.76 (((~![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, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))) | (~holds(holding(d), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))) | holds(on(d, c), do(putdown(d, c), do(pickup(d), do(putdown(c, table), do(pickup(c), 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(c), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))) | (~holds(holding(d), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))) | holds(on(d, c), do(putdown(d, c), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))))),
% 10.56/10.76 inference(rewrite,[status(thm)],[])).
% 10.56/10.76 tff(196,plain,
% 10.56/10.76 ((~![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, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))) | (~holds(holding(d), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))) | holds(on(d, c), do(putdown(d, c), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))))),
% 10.56/10.76 inference(quant_inst,[status(thm)],[])).
% 10.56/10.76 tff(197,plain,
% 10.56/10.76 ((~![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, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))) | (~holds(holding(d), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))) | holds(on(d, c), do(putdown(d, c), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))))),
% 10.56/10.76 inference(modus_ponens,[status(thm)],[196, 195])).
% 10.56/10.76 tff(198,plain,
% 10.56/10.76 (holds(on(d, c), do(putdown(d, c), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0)))))))),
% 10.56/10.76 inference(unit_resolution,[status(thm)],[197, 108, 194, 141])).
% 10.56/10.76 tff(199,plain,
% 10.56/10.76 (^[State: $i] : refl((~holds(on(d, c), State)) <=> (~holds(on(d, c), State)))),
% 10.56/10.76 inference(bind,[status(th)],[])).
% 10.56/10.76 tff(200,plain,
% 10.56/10.76 (![State: $i] : (~holds(on(d, c), State)) <=> ![State: $i] : (~holds(on(d, c), State))),
% 10.56/10.76 inference(quant_intro,[status(thm)],[199])).
% 10.56/10.76 tff(201,plain,
% 10.56/10.76 (![State: $i] : (~holds(on(d, c), State)) <=> ![State: $i] : (~holds(on(d, c), State))),
% 10.56/10.76 inference(rewrite,[status(thm)],[])).
% 10.56/10.76 tff(202,axiom,(![State: $i] : (~holds(on(d, c), State))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_DC')).
% 10.56/10.76 tff(203,plain,
% 10.56/10.76 (![State: $i] : (~holds(on(d, c), State))),
% 10.56/10.76 inference(modus_ponens,[status(thm)],[202, 201])).
% 10.56/10.76 tff(204,plain,(
% 10.56/10.76 ![State: $i] : (~holds(on(d, c), State))),
% 10.56/10.76 inference(skolemize,[status(sab)],[203])).
% 10.56/10.76 tff(205,plain,
% 10.56/10.76 (![State: $i] : (~holds(on(d, c), State))),
% 10.56/10.76 inference(modus_ponens,[status(thm)],[204, 200])).
% 10.56/10.76 tff(206,plain,
% 10.56/10.76 ((~![State: $i] : (~holds(on(d, c), State))) | (~holds(on(d, c), do(putdown(d, c), do(pickup(d), do(putdown(c, table), do(pickup(c), do(putdown(c, table), do(pickup(c), s0))))))))),
% 10.56/10.76 inference(quant_inst,[status(thm)],[])).
% 10.56/10.76 tff(207,plain,
% 10.56/10.76 ($false),
% 10.56/10.76 inference(unit_resolution,[status(thm)],[206, 205, 198])).
% 10.56/10.76 % SZS output end Proof
% 10.56/10.77 % E exiting
%------------------------------------------------------------------------------