%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CSR016+1 : TPTP v9.0.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:01:13 AM UTC 2025
% Result : Theorem 6.45s 6.63s
% Output : Proof 6.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CSR016+1 : TPTP v9.0.0. Bugfixed v3.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 12:30:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 6.45/6.63 % SZS status Theorem
% 6.45/6.63 % SZS output start Proof
% 6.45/6.63 tff(happens_type, type, (
% 6.45/6.63 happens: ( $i * $i ) > $o)).
% 6.45/6.63 tff(n0_type, type, (
% 6.45/6.63 n0: $i)).
% 6.45/6.63 tff(push_type, type, (
% 6.45/6.63 push: $i)).
% 6.45/6.63 tff(spinning_type, type, (
% 6.45/6.63 spinning: $i)).
% 6.45/6.63 tff(forwards_type, type, (
% 6.45/6.63 forwards: $i)).
% 6.45/6.63 tff(pull_type, type, (
% 6.45/6.63 pull: $i)).
% 6.45/6.63 tff(backwards_type, type, (
% 6.45/6.63 backwards: $i)).
% 6.45/6.63 tff(initiates_type, type, (
% 6.45/6.63 initiates: ( $i * $i * $i ) > $o)).
% 6.45/6.63 tff(n2_type, type, (
% 6.45/6.63 n2: $i)).
% 6.45/6.63 tff(n1_type, type, (
% 6.45/6.63 n1: $i)).
% 6.45/6.63 tff(less_type, type, (
% 6.45/6.63 less: ( $i * $i ) > $o)).
% 6.45/6.63 tff(less_or_equal_type, type, (
% 6.45/6.63 less_or_equal: ( $i * $i ) > $o)).
% 6.45/6.63 tff(holdsAt_type, type, (
% 6.45/6.63 holdsAt: ( $i * $i ) > $o)).
% 6.45/6.63 tff(plus_type, type, (
% 6.45/6.63 plus: ( $i * $i ) > $i)).
% 6.45/6.63 tff(1,plain,
% 6.45/6.63 ((n1 = n0) <=> (n0 = n1)),
% 6.45/6.63 inference(commutativity,[status(thm)],[])).
% 6.45/6.63 tff(2,plain,
% 6.45/6.63 ((~(n1 = n0)) <=> (~(n0 = n1))),
% 6.45/6.63 inference(monotonicity,[status(thm)],[1])).
% 6.45/6.63 tff(3,plain,
% 6.45/6.63 (^[X: $i, Y: $i] : refl((~(((Y = X) | less(Y, X)) <=> less(X, Y))) <=> (~(((Y = X) | less(Y, X)) <=> less(X, Y))))),
% 6.45/6.63 inference(bind,[status(th)],[])).
% 6.45/6.63 tff(4,plain,
% 6.45/6.63 (![X: $i, Y: $i] : (~(((Y = X) | less(Y, X)) <=> less(X, Y))) <=> ![X: $i, Y: $i] : (~(((Y = X) | less(Y, X)) <=> less(X, Y)))),
% 6.45/6.63 inference(quant_intro,[status(thm)],[3])).
% 6.45/6.63 tff(5,plain,
% 6.45/6.63 (^[X: $i, Y: $i] : trans(trans(monotonicity(rewrite(((~less(Y, X)) & (~(Y = X))) <=> (~((Y = X) | less(Y, X)))), ((less(X, Y) <=> ((~less(Y, X)) & (~(Y = X)))) <=> (less(X, Y) <=> (~((Y = X) | less(Y, X)))))), rewrite((less(X, Y) <=> (~((Y = X) | less(Y, X)))) <=> (~(((Y = X) | less(Y, X)) <=> less(X, Y)))), ((less(X, Y) <=> ((~less(Y, X)) & (~(Y = X)))) <=> (~(((Y = X) | less(Y, X)) <=> less(X, Y))))), rewrite((~(((Y = X) | less(Y, X)) <=> less(X, Y))) <=> (~(((Y = X) | less(Y, X)) <=> less(X, Y)))), ((less(X, Y) <=> ((~less(Y, X)) & (~(Y = X)))) <=> (~(((Y = X) | less(Y, X)) <=> less(X, Y)))))),
% 6.45/6.63 inference(bind,[status(th)],[])).
% 6.45/6.63 tff(6,plain,
% 6.45/6.63 (![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X)))) <=> ![X: $i, Y: $i] : (~(((Y = X) | less(Y, X)) <=> less(X, Y)))),
% 6.45/6.63 inference(quant_intro,[status(thm)],[5])).
% 6.45/6.63 tff(7,plain,
% 6.45/6.63 (![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X)))) <=> ![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(8,axiom,(![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','less_property')).
% 6.45/6.63 tff(9,plain,
% 6.45/6.63 (![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[8, 7])).
% 6.45/6.63 tff(10,plain,(
% 6.45/6.63 ![X: $i, Y: $i] : (less(X, Y) <=> ((~less(Y, X)) & (~(Y = X))))),
% 6.45/6.63 inference(skolemize,[status(sab)],[9])).
% 6.45/6.63 tff(11,plain,
% 6.45/6.63 (![X: $i, Y: $i] : (~(((Y = X) | less(Y, X)) <=> less(X, Y)))),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[10, 6])).
% 6.45/6.63 tff(12,plain,
% 6.45/6.63 (![X: $i, Y: $i] : (~(((Y = X) | less(Y, X)) <=> less(X, Y)))),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[11, 4])).
% 6.45/6.63 tff(13,plain,
% 6.45/6.63 ((~![X: $i, Y: $i] : (~(((Y = X) | less(Y, X)) <=> less(X, Y)))) | (~(((n1 = n0) | less(n1, n0)) <=> less(n0, n1)))),
% 6.45/6.63 inference(quant_inst,[status(thm)],[])).
% 6.45/6.63 tff(14,plain,
% 6.45/6.63 (~(((n1 = n0) | less(n1, n0)) <=> less(n0, n1))),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[13, 12])).
% 6.45/6.63 tff(15,plain,
% 6.45/6.63 (^[X: $i] : refl((less(X, n1) <=> less_or_equal(X, n0)) <=> (less(X, n1) <=> less_or_equal(X, n0)))),
% 6.45/6.63 inference(bind,[status(th)],[])).
% 6.45/6.63 tff(16,plain,
% 6.45/6.63 (![X: $i] : (less(X, n1) <=> less_or_equal(X, n0)) <=> ![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))),
% 6.45/6.63 inference(quant_intro,[status(thm)],[15])).
% 6.45/6.63 tff(17,plain,
% 6.45/6.63 (![X: $i] : (less(X, n1) <=> less_or_equal(X, n0)) <=> ![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(18,axiom,(![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','less1')).
% 6.45/6.63 tff(19,plain,
% 6.45/6.63 (![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[18, 17])).
% 6.45/6.63 tff(20,plain,(
% 6.45/6.63 ![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))),
% 6.45/6.63 inference(skolemize,[status(sab)],[19])).
% 6.45/6.63 tff(21,plain,
% 6.45/6.63 (![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[20, 16])).
% 6.45/6.63 tff(22,plain,
% 6.45/6.63 ((~![X: $i] : (less(X, n1) <=> less_or_equal(X, n0))) | (less(n0, n1) <=> less_or_equal(n0, n0))),
% 6.45/6.63 inference(quant_inst,[status(thm)],[])).
% 6.45/6.63 tff(23,plain,
% 6.45/6.63 (less(n0, n1) <=> less_or_equal(n0, n0)),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[22, 21])).
% 6.45/6.63 tff(24,plain,
% 6.45/6.63 (^[X: $i, Y: $i] : refl((less_or_equal(X, Y) <=> ((X = Y) | less(X, Y))) <=> (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y))))),
% 6.45/6.63 inference(bind,[status(th)],[])).
% 6.45/6.63 tff(25,plain,
% 6.45/6.63 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y))) <=> ![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 6.45/6.63 inference(quant_intro,[status(thm)],[24])).
% 6.45/6.63 tff(26,plain,
% 6.45/6.63 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y))) <=> ![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(27,plain,
% 6.45/6.63 (^[X: $i, Y: $i] : rewrite((less_or_equal(X, Y) <=> (less(X, Y) | (X = Y))) <=> (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y))))),
% 6.45/6.63 inference(bind,[status(th)],[])).
% 6.45/6.63 tff(28,plain,
% 6.45/6.63 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> (less(X, Y) | (X = Y))) <=> ![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 6.45/6.63 inference(quant_intro,[status(thm)],[27])).
% 6.45/6.63 tff(29,axiom,(![X: $i, Y: $i] : (less_or_equal(X, Y) <=> (less(X, Y) | (X = Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','less_or_equal')).
% 6.45/6.63 tff(30,plain,
% 6.45/6.63 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[29, 28])).
% 6.45/6.63 tff(31,plain,
% 6.45/6.63 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[30, 26])).
% 6.45/6.63 tff(32,plain,(
% 6.45/6.63 ![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 6.45/6.63 inference(skolemize,[status(sab)],[31])).
% 6.45/6.63 tff(33,plain,
% 6.45/6.63 (![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[32, 25])).
% 6.45/6.63 tff(34,plain,
% 6.45/6.63 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n0, n0)) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n0, n0))),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(35,plain,
% 6.45/6.63 ((less_or_equal(n0, n0) <=> $true) <=> less_or_equal(n0, n0)),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(36,plain,
% 6.45/6.63 (($true | less(n0, n0)) <=> $true),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(37,plain,
% 6.45/6.63 ((n0 = n0) <=> $true),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(38,plain,
% 6.45/6.63 (((n0 = n0) | less(n0, n0)) <=> ($true | less(n0, n0))),
% 6.45/6.63 inference(monotonicity,[status(thm)],[37])).
% 6.45/6.63 tff(39,plain,
% 6.45/6.63 (((n0 = n0) | less(n0, n0)) <=> $true),
% 6.45/6.63 inference(transitivity,[status(thm)],[38, 36])).
% 6.45/6.63 tff(40,plain,
% 6.45/6.63 ((less_or_equal(n0, n0) <=> ((n0 = n0) | less(n0, n0))) <=> (less_or_equal(n0, n0) <=> $true)),
% 6.45/6.63 inference(monotonicity,[status(thm)],[39])).
% 6.45/6.63 tff(41,plain,
% 6.45/6.63 ((less_or_equal(n0, n0) <=> ((n0 = n0) | less(n0, n0))) <=> less_or_equal(n0, n0)),
% 6.45/6.63 inference(transitivity,[status(thm)],[40, 35])).
% 6.45/6.63 tff(42,plain,
% 6.45/6.63 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(n0, n0) <=> ((n0 = n0) | less(n0, n0)))) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n0, n0))),
% 6.45/6.63 inference(monotonicity,[status(thm)],[41])).
% 6.45/6.63 tff(43,plain,
% 6.45/6.63 (((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(n0, n0) <=> ((n0 = n0) | less(n0, n0)))) <=> ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n0, n0))),
% 6.45/6.63 inference(transitivity,[status(thm)],[42, 34])).
% 6.45/6.63 tff(44,plain,
% 6.45/6.63 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(n0, n0) <=> ((n0 = n0) | less(n0, n0)))),
% 6.45/6.63 inference(quant_inst,[status(thm)],[])).
% 6.45/6.63 tff(45,plain,
% 6.45/6.63 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | less_or_equal(n0, n0)),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[44, 43])).
% 6.45/6.63 tff(46,plain,
% 6.45/6.63 (less_or_equal(n0, n0)),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[45, 33])).
% 6.45/6.63 tff(47,plain,
% 6.45/6.63 ((~(less(n0, n1) <=> less_or_equal(n0, n0))) | less(n0, n1) | (~less_or_equal(n0, n0))),
% 6.45/6.63 inference(tautology,[status(thm)],[])).
% 6.45/6.63 tff(48,plain,
% 6.45/6.63 (less(n0, n1)),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[47, 46, 23])).
% 6.45/6.63 tff(49,plain,
% 6.45/6.63 ((((n1 = n0) | less(n1, n0)) <=> less(n0, n1)) | (~((n1 = n0) | less(n1, n0))) | (~less(n0, n1))),
% 6.45/6.63 inference(tautology,[status(thm)],[])).
% 6.45/6.63 tff(50,plain,
% 6.45/6.63 (~((n1 = n0) | less(n1, n0))),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[49, 48, 14])).
% 6.45/6.63 tff(51,plain,
% 6.45/6.63 (((n1 = n0) | less(n1, n0)) | (~(n1 = n0))),
% 6.45/6.63 inference(tautology,[status(thm)],[])).
% 6.45/6.63 tff(52,plain,
% 6.45/6.63 (~(n1 = n0)),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[51, 50])).
% 6.45/6.63 tff(53,plain,
% 6.45/6.63 (~(n0 = n1)),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[52, 2])).
% 6.45/6.63 tff(54,plain,
% 6.45/6.63 ((n2 = n0) <=> (n0 = n2)),
% 6.45/6.63 inference(commutativity,[status(thm)],[])).
% 6.45/6.63 tff(55,plain,
% 6.45/6.63 ((~(n2 = n0)) <=> (~(n0 = n2))),
% 6.45/6.63 inference(monotonicity,[status(thm)],[54])).
% 6.45/6.63 tff(56,plain,
% 6.45/6.63 ((~![X: $i, Y: $i] : (~(((Y = X) | less(Y, X)) <=> less(X, Y)))) | (~(((n2 = n0) | less(n2, n0)) <=> less(n0, n2)))),
% 6.45/6.63 inference(quant_inst,[status(thm)],[])).
% 6.45/6.63 tff(57,plain,
% 6.45/6.63 (~(((n2 = n0) | less(n2, n0)) <=> less(n0, n2))),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[56, 12])).
% 6.45/6.63 tff(58,plain,
% 6.45/6.63 (^[X: $i] : refl((less(X, n2) <=> less_or_equal(X, n1)) <=> (less(X, n2) <=> less_or_equal(X, n1)))),
% 6.45/6.63 inference(bind,[status(th)],[])).
% 6.45/6.63 tff(59,plain,
% 6.45/6.63 (![X: $i] : (less(X, n2) <=> less_or_equal(X, n1)) <=> ![X: $i] : (less(X, n2) <=> less_or_equal(X, n1))),
% 6.45/6.63 inference(quant_intro,[status(thm)],[58])).
% 6.45/6.63 tff(60,plain,
% 6.45/6.63 (![X: $i] : (less(X, n2) <=> less_or_equal(X, n1)) <=> ![X: $i] : (less(X, n2) <=> less_or_equal(X, n1))),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(61,axiom,(![X: $i] : (less(X, n2) <=> less_or_equal(X, n1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','less2')).
% 6.45/6.63 tff(62,plain,
% 6.45/6.63 (![X: $i] : (less(X, n2) <=> less_or_equal(X, n1))),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[61, 60])).
% 6.45/6.63 tff(63,plain,(
% 6.45/6.63 ![X: $i] : (less(X, n2) <=> less_or_equal(X, n1))),
% 6.45/6.63 inference(skolemize,[status(sab)],[62])).
% 6.45/6.63 tff(64,plain,
% 6.45/6.63 (![X: $i] : (less(X, n2) <=> less_or_equal(X, n1))),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[63, 59])).
% 6.45/6.63 tff(65,plain,
% 6.45/6.63 ((~![X: $i] : (less(X, n2) <=> less_or_equal(X, n1))) | (less(n0, n2) <=> less_or_equal(n0, n1))),
% 6.45/6.63 inference(quant_inst,[status(thm)],[])).
% 6.45/6.63 tff(66,plain,
% 6.45/6.63 (less(n0, n2) <=> less_or_equal(n0, n1)),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[65, 64])).
% 6.45/6.63 tff(67,plain,
% 6.45/6.63 ((~![X: $i, Y: $i] : (less_or_equal(X, Y) <=> ((X = Y) | less(X, Y)))) | (less_or_equal(n0, n1) <=> ((n0 = n1) | less(n0, n1)))),
% 6.45/6.63 inference(quant_inst,[status(thm)],[])).
% 6.45/6.63 tff(68,plain,
% 6.45/6.63 (less_or_equal(n0, n1) <=> ((n0 = n1) | less(n0, n1))),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[67, 33])).
% 6.45/6.63 tff(69,plain,
% 6.45/6.63 ((~![X: $i, Y: $i] : (~(((Y = X) | less(Y, X)) <=> less(X, Y)))) | (~(((n0 = n1) | less(n0, n1)) <=> less(n1, n0)))),
% 6.45/6.63 inference(quant_inst,[status(thm)],[])).
% 6.45/6.63 tff(70,plain,
% 6.45/6.63 (~(((n0 = n1) | less(n0, n1)) <=> less(n1, n0))),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[69, 12])).
% 6.45/6.63 tff(71,assumption,(less(n1, n0)), introduced(assumption)).
% 6.45/6.63 tff(72,plain,
% 6.45/6.63 (^[X: $i] : refl((~less(X, n0)) <=> (~less(X, n0)))),
% 6.45/6.63 inference(bind,[status(th)],[])).
% 6.45/6.63 tff(73,plain,
% 6.45/6.63 (![X: $i] : (~less(X, n0)) <=> ![X: $i] : (~less(X, n0))),
% 6.45/6.63 inference(quant_intro,[status(thm)],[72])).
% 6.45/6.63 tff(74,plain,
% 6.45/6.63 ((~?[X: $i] : less(X, n0)) <=> (~?[X: $i] : less(X, n0))),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(75,axiom,(~?[X: $i] : less(X, n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','less0')).
% 6.45/6.63 tff(76,plain,
% 6.45/6.63 (~?[X: $i] : less(X, n0)),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[75, 74])).
% 6.45/6.63 tff(77,plain,
% 6.45/6.63 (~?[X: $i] : less(X, n0)),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[76, 74])).
% 6.45/6.63 tff(78,plain,
% 6.45/6.63 (~?[X: $i] : less(X, n0)),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[77, 74])).
% 6.45/6.63 tff(79,plain,
% 6.45/6.63 (~?[X: $i] : less(X, n0)),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[78, 74])).
% 6.45/6.63 tff(80,plain,
% 6.45/6.63 (^[X: $i] : refl($oeq((~less(X, n0)), (~less(X, n0))))),
% 6.45/6.63 inference(bind,[status(th)],[])).
% 6.45/6.63 tff(81,plain,(
% 6.45/6.63 ![X: $i] : (~less(X, n0))),
% 6.45/6.63 inference(nnf-neg,[status(sab)],[79, 80])).
% 6.45/6.63 tff(82,plain,
% 6.45/6.63 (![X: $i] : (~less(X, n0))),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[81, 73])).
% 6.45/6.63 tff(83,plain,
% 6.45/6.63 ((~![X: $i] : (~less(X, n0))) | (~less(n1, n0))),
% 6.45/6.63 inference(quant_inst,[status(thm)],[])).
% 6.45/6.63 tff(84,plain,
% 6.45/6.63 ($false),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[83, 82, 71])).
% 6.45/6.63 tff(85,plain,(~less(n1, n0)), inference(lemma,lemma(discharge,[]))).
% 6.45/6.63 tff(86,plain,
% 6.45/6.63 ((((n0 = n1) | less(n0, n1)) <=> less(n1, n0)) | ((n0 = n1) | less(n0, n1)) | less(n1, n0)),
% 6.45/6.63 inference(tautology,[status(thm)],[])).
% 6.45/6.63 tff(87,plain,
% 6.45/6.63 ((((n0 = n1) | less(n0, n1)) <=> less(n1, n0)) | ((n0 = n1) | less(n0, n1))),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[86, 85])).
% 6.45/6.63 tff(88,plain,
% 6.45/6.63 ((n0 = n1) | less(n0, n1)),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[87, 70])).
% 6.45/6.63 tff(89,plain,
% 6.45/6.63 ((~(less_or_equal(n0, n1) <=> ((n0 = n1) | less(n0, n1)))) | less_or_equal(n0, n1) | (~((n0 = n1) | less(n0, n1)))),
% 6.45/6.63 inference(tautology,[status(thm)],[])).
% 6.45/6.63 tff(90,plain,
% 6.45/6.63 ((~(less_or_equal(n0, n1) <=> ((n0 = n1) | less(n0, n1)))) | less_or_equal(n0, n1)),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[89, 88])).
% 6.45/6.63 tff(91,plain,
% 6.45/6.63 (less_or_equal(n0, n1)),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[90, 68])).
% 6.45/6.63 tff(92,plain,
% 6.45/6.63 ((~(less(n0, n2) <=> less_or_equal(n0, n1))) | less(n0, n2) | (~less_or_equal(n0, n1))),
% 6.45/6.63 inference(tautology,[status(thm)],[])).
% 6.45/6.63 tff(93,plain,
% 6.45/6.63 ((~(less(n0, n2) <=> less_or_equal(n0, n1))) | less(n0, n2)),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[92, 91])).
% 6.45/6.63 tff(94,plain,
% 6.45/6.63 (less(n0, n2)),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[93, 66])).
% 6.45/6.63 tff(95,plain,
% 6.45/6.63 ((((n2 = n0) | less(n2, n0)) <=> less(n0, n2)) | (~((n2 = n0) | less(n2, n0))) | (~less(n0, n2))),
% 6.45/6.63 inference(tautology,[status(thm)],[])).
% 6.45/6.63 tff(96,plain,
% 6.45/6.63 ((((n2 = n0) | less(n2, n0)) <=> less(n0, n2)) | (~((n2 = n0) | less(n2, n0)))),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[95, 94])).
% 6.45/6.63 tff(97,plain,
% 6.45/6.63 (~((n2 = n0) | less(n2, n0))),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[96, 57])).
% 6.45/6.63 tff(98,plain,
% 6.45/6.63 (((n2 = n0) | less(n2, n0)) | (~(n2 = n0))),
% 6.45/6.63 inference(tautology,[status(thm)],[])).
% 6.45/6.63 tff(99,plain,
% 6.45/6.63 (~(n2 = n0)),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[98, 97])).
% 6.45/6.63 tff(100,plain,
% 6.45/6.63 (~(n0 = n2)),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[99, 55])).
% 6.45/6.63 tff(101,plain,
% 6.45/6.63 ((pull = push) <=> (push = pull)),
% 6.45/6.63 inference(commutativity,[status(thm)],[])).
% 6.45/6.63 tff(102,plain,
% 6.45/6.63 ((push = pull) <=> (pull = push)),
% 6.45/6.63 inference(symmetry,[status(thm)],[101])).
% 6.45/6.63 tff(103,plain,
% 6.45/6.63 ((~(push = pull)) <=> (~(pull = push))),
% 6.45/6.63 inference(monotonicity,[status(thm)],[102])).
% 6.45/6.63 tff(104,plain,
% 6.45/6.63 ((~(push = pull)) <=> (~(push = pull))),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(105,axiom,(~(push = pull)), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax','push_not_pull')).
% 6.45/6.63 tff(106,plain,
% 6.45/6.63 (~(push = pull)),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[105, 104])).
% 6.45/6.63 tff(107,plain,
% 6.45/6.63 (~(pull = push)),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[106, 103])).
% 6.45/6.63 tff(108,plain,
% 6.45/6.63 (((~(pull = push)) | (~(n0 = n2))) | (pull = push)),
% 6.45/6.63 inference(tautology,[status(thm)],[])).
% 6.45/6.63 tff(109,plain,
% 6.45/6.63 ((~(pull = push)) | (~(n0 = n2))),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[108, 107])).
% 6.45/6.63 tff(110,plain,
% 6.45/6.63 ((~((pull = push) | (n0 = n2) | (n0 = n1) | (~((~(pull = push)) | (~(n0 = n2)))))) | (pull = push) | (n0 = n2) | (n0 = n1) | (~((~(pull = push)) | (~(n0 = n2))))),
% 6.45/6.63 inference(tautology,[status(thm)],[])).
% 6.45/6.63 tff(111,plain,
% 6.45/6.63 ((~((pull = push) | (n0 = n2) | (n0 = n1) | (~((~(pull = push)) | (~(n0 = n2)))))) | (n0 = n2) | (n0 = n1)),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[110, 107, 109])).
% 6.45/6.63 tff(112,plain,
% 6.45/6.63 (~((pull = push) | (n0 = n2) | (n0 = n1) | (~((~(pull = push)) | (~(n0 = n2)))))),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[111, 100, 53])).
% 6.45/6.63 tff(113,assumption,(~(happens(pull, n0) <=> ((pull = push) | (n0 = n2) | (n0 = n1) | (~((~(pull = push)) | (~(n0 = n2))))))), introduced(assumption)).
% 6.45/6.63 tff(114,plain,
% 6.45/6.63 (^[Event: $i, Time: $i] : refl((happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))))) <=> (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))))))),
% 6.45/6.63 inference(bind,[status(th)],[])).
% 6.45/6.63 tff(115,plain,
% 6.45/6.63 (![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))),
% 6.45/6.63 inference(quant_intro,[status(thm)],[114])).
% 6.45/6.63 tff(116,plain,
% 6.45/6.63 (^[Event: $i, Time: $i] : rewrite((happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)))) <=> (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0)))))))),
% 6.45/6.63 inference(bind,[status(th)],[])).
% 6.45/6.63 tff(117,plain,
% 6.45/6.63 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))),
% 6.45/6.63 inference(quant_intro,[status(thm)],[116])).
% 6.45/6.63 tff(118,plain,
% 6.45/6.63 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(119,plain,
% 6.45/6.63 (^[Event: $i, Time: $i] : rewrite((happens(Event, Time) <=> (((((Event = push) & (Time = n0)) | ((Event = pull) & (Time = n1))) | ((Event = pull) & (Time = n2))) | ((Event = push) & (Time = n2)))) <=> (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0)))))),
% 6.45/6.63 inference(bind,[status(th)],[])).
% 6.45/6.63 tff(120,plain,
% 6.45/6.63 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((((Event = push) & (Time = n0)) | ((Event = pull) & (Time = n1))) | ((Event = pull) & (Time = n2))) | ((Event = push) & (Time = n2)))) <=> ![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 6.45/6.63 inference(quant_intro,[status(thm)],[119])).
% 6.45/6.63 tff(121,axiom,(![Event: $i, Time: $i] : (happens(Event, Time) <=> (((((Event = push) & (Time = n0)) | ((Event = pull) & (Time = n1))) | ((Event = pull) & (Time = n2))) | ((Event = push) & (Time = n2))))), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax','happens_all_defn')).
% 6.45/6.63 tff(122,plain,
% 6.45/6.63 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[121, 120])).
% 6.45/6.63 tff(123,plain,
% 6.45/6.63 (![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[122, 118])).
% 6.45/6.63 tff(124,plain,(
% 6.45/6.63 ![Event: $i, Time: $i] : (happens(Event, Time) <=> (((Event = push) & (Time = n2)) | ((Event = pull) & (Time = n2)) | ((Event = pull) & (Time = n1)) | ((Event = push) & (Time = n0))))),
% 6.45/6.63 inference(skolemize,[status(sab)],[123])).
% 6.45/6.63 tff(125,plain,
% 6.45/6.63 (![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[124, 117])).
% 6.45/6.63 tff(126,plain,
% 6.45/6.63 (![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[125, 115])).
% 6.45/6.63 tff(127,plain,
% 6.45/6.63 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | (happens(pull, n0) <=> ((pull = push) | (n0 = n2) | (n0 = n1) | (~((~(pull = push)) | (~(n0 = n2))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | (happens(pull, n0) <=> ((pull = push) | (n0 = n2) | (n0 = n1) | (~((~(pull = push)) | (~(n0 = n2)))))))),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(128,plain,
% 6.45/6.63 ((happens(pull, n0) <=> ((~((~(pull = push)) | (~(n0 = n2)))) | (~((~(n0 = n2)) | (~(pull = pull)))) | (~((~(pull = pull)) | (~(n0 = n1)))) | (~((~(pull = push)) | (~(n0 = n0)))))) <=> (happens(pull, n0) <=> ((pull = push) | (n0 = n2) | (n0 = n1) | (~((~(pull = push)) | (~(n0 = n2))))))),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(129,plain,
% 6.45/6.63 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | (happens(pull, n0) <=> ((~((~(pull = push)) | (~(n0 = n2)))) | (~((~(n0 = n2)) | (~(pull = pull)))) | (~((~(pull = pull)) | (~(n0 = n1)))) | (~((~(pull = push)) | (~(n0 = n0))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | (happens(pull, n0) <=> ((pull = push) | (n0 = n2) | (n0 = n1) | (~((~(pull = push)) | (~(n0 = n2)))))))),
% 6.45/6.63 inference(monotonicity,[status(thm)],[128])).
% 6.45/6.63 tff(130,plain,
% 6.45/6.63 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | (happens(pull, n0) <=> ((~((~(pull = push)) | (~(n0 = n2)))) | (~((~(n0 = n2)) | (~(pull = pull)))) | (~((~(pull = pull)) | (~(n0 = n1)))) | (~((~(pull = push)) | (~(n0 = n0))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | (happens(pull, n0) <=> ((pull = push) | (n0 = n2) | (n0 = n1) | (~((~(pull = push)) | (~(n0 = n2)))))))),
% 6.45/6.63 inference(transitivity,[status(thm)],[129, 127])).
% 6.45/6.63 tff(131,plain,
% 6.45/6.63 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | (happens(pull, n0) <=> ((~((~(pull = push)) | (~(n0 = n2)))) | (~((~(n0 = n2)) | (~(pull = pull)))) | (~((~(pull = pull)) | (~(n0 = n1)))) | (~((~(pull = push)) | (~(n0 = n0))))))),
% 6.45/6.63 inference(quant_inst,[status(thm)],[])).
% 6.45/6.63 tff(132,plain,
% 6.45/6.63 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | (happens(pull, n0) <=> ((pull = push) | (n0 = n2) | (n0 = n1) | (~((~(pull = push)) | (~(n0 = n2))))))),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[131, 130])).
% 6.45/6.63 tff(133,plain,
% 6.45/6.63 ($false),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[132, 126, 113])).
% 6.45/6.63 tff(134,plain,(happens(pull, n0) <=> ((pull = push) | (n0 = n2) | (n0 = n1) | (~((~(pull = push)) | (~(n0 = n2)))))), inference(lemma,lemma(discharge,[]))).
% 6.45/6.63 tff(135,plain,
% 6.45/6.63 ((~(happens(pull, n0) <=> ((pull = push) | (n0 = n2) | (n0 = n1) | (~((~(pull = push)) | (~(n0 = n2))))))) | (~happens(pull, n0)) | ((pull = push) | (n0 = n2) | (n0 = n1) | (~((~(pull = push)) | (~(n0 = n2)))))),
% 6.45/6.63 inference(tautology,[status(thm)],[])).
% 6.45/6.63 tff(136,plain,
% 6.45/6.63 ((~happens(pull, n0)) | ((pull = push) | (n0 = n2) | (n0 = n1) | (~((~(pull = push)) | (~(n0 = n2)))))),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[135, 134])).
% 6.45/6.63 tff(137,plain,
% 6.45/6.63 (~happens(pull, n0)),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[136, 112])).
% 6.45/6.63 tff(138,plain,
% 6.45/6.63 (((~happens(pull, n0)) | (~((~(push = pull)) | (~(forwards = backwards)) | happens(push, n0))) | (~((~(push = pull)) | (~(forwards = spinning)) | (~happens(push, n0))))) | happens(pull, n0)),
% 6.45/6.63 inference(tautology,[status(thm)],[])).
% 6.45/6.63 tff(139,plain,
% 6.45/6.63 ((~happens(pull, n0)) | (~((~(push = pull)) | (~(forwards = backwards)) | happens(push, n0))) | (~((~(push = pull)) | (~(forwards = spinning)) | (~happens(push, n0))))),
% 6.45/6.63 inference(unit_resolution,[status(thm)],[138, 137])).
% 6.45/6.63 tff(140,assumption,(initiates(push, forwards, n0)), introduced(assumption)).
% 6.45/6.63 tff(141,plain,
% 6.45/6.63 ((plus(n0, n1) = n1) <=> (plus(n0, n1) = n1)),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(142,axiom,(plus(n0, n1) = n1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus0_1')).
% 6.45/6.63 tff(143,plain,
% 6.45/6.63 (plus(n0, n1) = n1),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[142, 141])).
% 6.45/6.63 tff(144,plain,
% 6.45/6.63 (holdsAt(forwards, plus(n0, n1)) <=> holdsAt(forwards, n1)),
% 6.45/6.63 inference(monotonicity,[status(thm)],[143])).
% 6.45/6.63 tff(145,plain,
% 6.45/6.63 (holdsAt(forwards, n1) <=> holdsAt(forwards, plus(n0, n1))),
% 6.45/6.63 inference(symmetry,[status(thm)],[144])).
% 6.45/6.63 tff(146,plain,
% 6.45/6.63 ((~holdsAt(forwards, n1)) <=> (~holdsAt(forwards, plus(n0, n1)))),
% 6.45/6.63 inference(monotonicity,[status(thm)],[145])).
% 6.45/6.63 tff(147,plain,
% 6.45/6.63 ((~holdsAt(forwards, n1)) <=> (~holdsAt(forwards, n1))),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(148,axiom,(~holdsAt(forwards, n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','forwards_1')).
% 6.45/6.63 tff(149,plain,
% 6.45/6.63 (~holdsAt(forwards, n1)),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[148, 147])).
% 6.45/6.63 tff(150,plain,
% 6.45/6.63 (~holdsAt(forwards, plus(n0, n1))),
% 6.45/6.63 inference(modus_ponens,[status(thm)],[149, 146])).
% 6.45/6.63 tff(151,plain,
% 6.45/6.63 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | happens(push, n0)) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | happens(push, n0))),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(152,plain,
% 6.45/6.63 ((happens(push, n0) <=> $true) <=> happens(push, n0)),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(153,plain,
% 6.45/6.63 (((n0 = n2) | (~((~(n0 = n2)) | (~(push = pull)))) | (~((~(push = pull)) | (~(n0 = n1)))) | $true) <=> $true),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.63 tff(154,plain,
% 6.45/6.63 ((~$false) <=> $true),
% 6.45/6.63 inference(rewrite,[status(thm)],[])).
% 6.45/6.64 tff(155,plain,
% 6.45/6.64 (($false | $false) <=> $false),
% 6.45/6.64 inference(rewrite,[status(thm)],[])).
% 6.45/6.64 tff(156,plain,
% 6.45/6.64 ((~$true) <=> $false),
% 6.45/6.64 inference(rewrite,[status(thm)],[])).
% 6.45/6.64 tff(157,plain,
% 6.45/6.64 ((~(n0 = n0)) <=> (~$true)),
% 6.45/6.64 inference(monotonicity,[status(thm)],[37])).
% 6.45/6.64 tff(158,plain,
% 6.45/6.64 ((~(n0 = n0)) <=> $false),
% 6.45/6.64 inference(transitivity,[status(thm)],[157, 156])).
% 6.45/6.64 tff(159,plain,
% 6.45/6.64 ((push = push) <=> $true),
% 6.45/6.64 inference(rewrite,[status(thm)],[])).
% 6.45/6.64 tff(160,plain,
% 6.45/6.64 ((~(push = push)) <=> (~$true)),
% 6.45/6.64 inference(monotonicity,[status(thm)],[159])).
% 6.45/6.64 tff(161,plain,
% 6.45/6.64 ((~(push = push)) <=> $false),
% 6.45/6.64 inference(transitivity,[status(thm)],[160, 156])).
% 6.45/6.64 tff(162,plain,
% 6.45/6.64 (((~(push = push)) | (~(n0 = n0))) <=> ($false | $false)),
% 6.45/6.64 inference(monotonicity,[status(thm)],[161, 158])).
% 6.45/6.64 tff(163,plain,
% 6.45/6.64 (((~(push = push)) | (~(n0 = n0))) <=> $false),
% 6.45/6.64 inference(transitivity,[status(thm)],[162, 155])).
% 6.45/6.64 tff(164,plain,
% 6.45/6.64 ((~((~(push = push)) | (~(n0 = n0)))) <=> (~$false)),
% 6.45/6.64 inference(monotonicity,[status(thm)],[163])).
% 6.45/6.64 tff(165,plain,
% 6.45/6.64 ((~((~(push = push)) | (~(n0 = n0)))) <=> $true),
% 6.45/6.64 inference(transitivity,[status(thm)],[164, 154])).
% 6.45/6.64 tff(166,plain,
% 6.45/6.64 ((~((~(push = pull)) | (~(n0 = n1)))) <=> (~((~(push = pull)) | (~(n0 = n1))))),
% 6.45/6.64 inference(rewrite,[status(thm)],[])).
% 6.45/6.64 tff(167,plain,
% 6.45/6.64 ((~(~(n0 = n2))) <=> (n0 = n2)),
% 6.45/6.64 inference(rewrite,[status(thm)],[])).
% 6.45/6.64 tff(168,plain,
% 6.45/6.64 (($false | (~(n0 = n2))) <=> (~(n0 = n2))),
% 6.45/6.64 inference(rewrite,[status(thm)],[])).
% 6.45/6.64 tff(169,plain,
% 6.45/6.64 (((~(push = push)) | (~(n0 = n2))) <=> ($false | (~(n0 = n2)))),
% 6.45/6.64 inference(monotonicity,[status(thm)],[161])).
% 6.45/6.64 tff(170,plain,
% 6.45/6.64 (((~(push = push)) | (~(n0 = n2))) <=> (~(n0 = n2))),
% 6.45/6.64 inference(transitivity,[status(thm)],[169, 168])).
% 6.45/6.64 tff(171,plain,
% 6.45/6.64 ((~((~(push = push)) | (~(n0 = n2)))) <=> (~(~(n0 = n2)))),
% 6.45/6.64 inference(monotonicity,[status(thm)],[170])).
% 6.45/6.64 tff(172,plain,
% 6.45/6.64 ((~((~(push = push)) | (~(n0 = n2)))) <=> (n0 = n2)),
% 6.45/6.64 inference(transitivity,[status(thm)],[171, 167])).
% 6.45/6.64 tff(173,plain,
% 6.45/6.64 (((~((~(push = push)) | (~(n0 = n2)))) | (~((~(n0 = n2)) | (~(push = pull)))) | (~((~(push = pull)) | (~(n0 = n1)))) | (~((~(push = push)) | (~(n0 = n0))))) <=> ((n0 = n2) | (~((~(n0 = n2)) | (~(push = pull)))) | (~((~(push = pull)) | (~(n0 = n1)))) | $true)),
% 6.45/6.64 inference(monotonicity,[status(thm)],[172, 166, 165])).
% 6.45/6.64 tff(174,plain,
% 6.45/6.64 (((~((~(push = push)) | (~(n0 = n2)))) | (~((~(n0 = n2)) | (~(push = pull)))) | (~((~(push = pull)) | (~(n0 = n1)))) | (~((~(push = push)) | (~(n0 = n0))))) <=> $true),
% 6.45/6.64 inference(transitivity,[status(thm)],[173, 153])).
% 6.45/6.64 tff(175,plain,
% 6.45/6.64 ((happens(push, n0) <=> ((~((~(push = push)) | (~(n0 = n2)))) | (~((~(n0 = n2)) | (~(push = pull)))) | (~((~(push = pull)) | (~(n0 = n1)))) | (~((~(push = push)) | (~(n0 = n0)))))) <=> (happens(push, n0) <=> $true)),
% 6.45/6.64 inference(monotonicity,[status(thm)],[174])).
% 6.45/6.64 tff(176,plain,
% 6.45/6.64 ((happens(push, n0) <=> ((~((~(push = push)) | (~(n0 = n2)))) | (~((~(n0 = n2)) | (~(push = pull)))) | (~((~(push = pull)) | (~(n0 = n1)))) | (~((~(push = push)) | (~(n0 = n0)))))) <=> happens(push, n0)),
% 6.45/6.64 inference(transitivity,[status(thm)],[175, 152])).
% 6.45/6.64 tff(177,plain,
% 6.45/6.64 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | (happens(push, n0) <=> ((~((~(push = push)) | (~(n0 = n2)))) | (~((~(n0 = n2)) | (~(push = pull)))) | (~((~(push = pull)) | (~(n0 = n1)))) | (~((~(push = push)) | (~(n0 = n0))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | happens(push, n0))),
% 6.45/6.64 inference(monotonicity,[status(thm)],[176])).
% 6.45/6.64 tff(178,plain,
% 6.45/6.64 (((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | (happens(push, n0) <=> ((~((~(push = push)) | (~(n0 = n2)))) | (~((~(n0 = n2)) | (~(push = pull)))) | (~((~(push = pull)) | (~(n0 = n1)))) | (~((~(push = push)) | (~(n0 = n0))))))) <=> ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | happens(push, n0))),
% 6.45/6.64 inference(transitivity,[status(thm)],[177, 151])).
% 6.45/6.64 tff(179,plain,
% 6.45/6.64 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | (happens(push, n0) <=> ((~((~(push = push)) | (~(n0 = n2)))) | (~((~(n0 = n2)) | (~(push = pull)))) | (~((~(push = pull)) | (~(n0 = n1)))) | (~((~(push = push)) | (~(n0 = n0))))))),
% 6.45/6.64 inference(quant_inst,[status(thm)],[])).
% 6.45/6.64 tff(180,plain,
% 6.45/6.64 ((~![Event: $i, Time: $i] : (happens(Event, Time) <=> ((~((~(Event = push)) | (~(Time = n2)))) | (~((~(Time = n2)) | (~(Event = pull)))) | (~((~(Event = pull)) | (~(Time = n1)))) | (~((~(Event = push)) | (~(Time = n0))))))) | happens(push, n0)),
% 6.45/6.64 inference(modus_ponens,[status(thm)],[179, 178])).
% 6.45/6.64 tff(181,plain,
% 6.45/6.64 (happens(push, n0)),
% 6.45/6.64 inference(unit_resolution,[status(thm)],[180, 126])).
% 6.45/6.64 tff(182,plain,
% 6.45/6.64 (^[Event: $i, Time: $i, Fluent: $i] : refl((holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time))) <=> (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time))))),
% 6.45/6.64 inference(bind,[status(th)],[])).
% 6.45/6.64 tff(183,plain,
% 6.45/6.64 (![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time))) <=> ![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))),
% 6.45/6.64 inference(quant_intro,[status(thm)],[182])).
% 6.45/6.64 tff(184,plain,
% 6.45/6.64 (^[Event: $i, Time: $i, Fluent: $i] : trans(monotonicity(trans(monotonicity(rewrite((happens(Event, Time) & initiates(Event, Fluent, Time)) <=> (~((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))))), ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) <=> (~(~((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))))))), rewrite((~(~((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))))) <=> ((~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))), ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) <=> ((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))))), (((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> (((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))))), rewrite((((~happens(Event, Time)) | (~initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))), (((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))))),
% 6.45/6.64 inference(bind,[status(th)],[])).
% 6.45/6.64 tff(185,plain,
% 6.45/6.64 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> ![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))),
% 6.45/6.64 inference(quant_intro,[status(thm)],[184])).
% 6.45/6.64 tff(186,plain,
% 6.45/6.64 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 6.45/6.64 inference(rewrite,[status(thm)],[])).
% 6.45/6.64 tff(187,plain,
% 6.45/6.64 (^[Event: $i, Time: $i, Fluent: $i] : rewrite(((happens(Event, Time) & initiates(Event, Fluent, Time)) => holdsAt(Fluent, plus(Time, n1))) <=> ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1))))),
% 6.45/6.64 inference(bind,[status(th)],[])).
% 6.45/6.64 tff(188,plain,
% 6.45/6.64 (![Event: $i, Time: $i, Fluent: $i] : ((happens(Event, Time) & initiates(Event, Fluent, Time)) => holdsAt(Fluent, plus(Time, n1))) <=> ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 6.45/6.64 inference(quant_intro,[status(thm)],[187])).
% 6.45/6.64 tff(189,axiom,(![Event: $i, Time: $i, Fluent: $i] : ((happens(Event, Time) & initiates(Event, Fluent, Time)) => holdsAt(Fluent, plus(Time, n1)))), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+0.ax','happens_holds')).
% 6.45/6.64 tff(190,plain,
% 6.45/6.64 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 6.45/6.64 inference(modus_ponens,[status(thm)],[189, 188])).
% 6.45/6.64 tff(191,plain,
% 6.45/6.64 (![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 6.45/6.64 inference(modus_ponens,[status(thm)],[190, 186])).
% 6.45/6.64 tff(192,plain,(
% 6.45/6.64 ![Event: $i, Time: $i, Fluent: $i] : ((~(happens(Event, Time) & initiates(Event, Fluent, Time))) | holdsAt(Fluent, plus(Time, n1)))),
% 6.45/6.64 inference(skolemize,[status(sab)],[191])).
% 6.45/6.64 tff(193,plain,
% 6.45/6.64 (![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))),
% 6.45/6.64 inference(modus_ponens,[status(thm)],[192, 185])).
% 6.45/6.64 tff(194,plain,
% 6.45/6.64 (![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))),
% 6.45/6.64 inference(modus_ponens,[status(thm)],[193, 183])).
% 6.45/6.64 tff(195,plain,
% 6.45/6.64 (((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | ((~happens(push, n0)) | (~initiates(push, forwards, n0)) | holdsAt(forwards, plus(n0, n1)))) <=> ((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | (~happens(push, n0)) | (~initiates(push, forwards, n0)) | holdsAt(forwards, plus(n0, n1)))),
% 6.45/6.64 inference(rewrite,[status(thm)],[])).
% 6.45/6.64 tff(196,plain,
% 6.45/6.64 ((holdsAt(forwards, plus(n0, n1)) | (~happens(push, n0)) | (~initiates(push, forwards, n0))) <=> ((~happens(push, n0)) | (~initiates(push, forwards, n0)) | holdsAt(forwards, plus(n0, n1)))),
% 6.45/6.64 inference(rewrite,[status(thm)],[])).
% 6.45/6.64 tff(197,plain,
% 6.45/6.64 (((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | (holdsAt(forwards, plus(n0, n1)) | (~happens(push, n0)) | (~initiates(push, forwards, n0)))) <=> ((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | ((~happens(push, n0)) | (~initiates(push, forwards, n0)) | holdsAt(forwards, plus(n0, n1))))),
% 6.45/6.64 inference(monotonicity,[status(thm)],[196])).
% 6.45/6.64 tff(198,plain,
% 6.45/6.64 (((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | (holdsAt(forwards, plus(n0, n1)) | (~happens(push, n0)) | (~initiates(push, forwards, n0)))) <=> ((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | (~happens(push, n0)) | (~initiates(push, forwards, n0)) | holdsAt(forwards, plus(n0, n1)))),
% 6.45/6.64 inference(transitivity,[status(thm)],[197, 195])).
% 6.45/6.64 tff(199,plain,
% 6.45/6.64 ((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | (holdsAt(forwards, plus(n0, n1)) | (~happens(push, n0)) | (~initiates(push, forwards, n0)))),
% 6.45/6.64 inference(quant_inst,[status(thm)],[])).
% 6.45/6.64 tff(200,plain,
% 6.45/6.64 ((~![Event: $i, Time: $i, Fluent: $i] : (holdsAt(Fluent, plus(Time, n1)) | (~happens(Event, Time)) | (~initiates(Event, Fluent, Time)))) | (~happens(push, n0)) | (~initiates(push, forwards, n0)) | holdsAt(forwards, plus(n0, n1))),
% 6.45/6.64 inference(modus_ponens,[status(thm)],[199, 198])).
% 6.45/6.64 tff(201,plain,
% 6.45/6.64 ((~initiates(push, forwards, n0)) | holdsAt(forwards, plus(n0, n1))),
% 6.45/6.64 inference(unit_resolution,[status(thm)],[200, 194, 181])).
% 6.45/6.64 tff(202,plain,
% 6.45/6.64 ($false),
% 6.45/6.64 inference(unit_resolution,[status(thm)],[201, 150, 140])).
% 6.45/6.64 tff(203,plain,(~initiates(push, forwards, n0)), inference(lemma,lemma(discharge,[]))).
% 6.45/6.64 tff(204,plain,
% 6.45/6.64 ((~(initiates(push, forwards, n0) <=> ((~happens(pull, n0)) | (~((~(push = pull)) | (~(forwards = backwards)) | happens(push, n0))) | (~((~(push = pull)) | (~(forwards = spinning)) | (~happens(push, n0))))))) | initiates(push, forwards, n0) | (~((~happens(pull, n0)) | (~((~(push = pull)) | (~(forwards = backwards)) | happens(push, n0))) | (~((~(push = pull)) | (~(forwards = spinning)) | (~happens(push, n0))))))),
% 6.45/6.64 inference(tautology,[status(thm)],[])).
% 6.45/6.64 tff(205,plain,
% 6.45/6.64 (~(initiates(push, forwards, n0) <=> ((~happens(pull, n0)) | (~((~(push = pull)) | (~(forwards = backwards)) | happens(push, n0))) | (~((~(push = pull)) | (~(forwards = spinning)) | (~happens(push, n0))))))),
% 6.45/6.64 inference(unit_resolution,[status(thm)],[204, 203, 139])).
% 6.45/6.64 tff(206,plain,
% 6.45/6.64 (^[Event: $i, Fluent: $i, Time: $i] : refl((initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning)))))) <=> (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning)))))))),
% 6.45/6.64 inference(bind,[status(th)],[])).
% 6.45/6.64 tff(207,plain,
% 6.45/6.64 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning)))))) <=> ![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))),
% 6.45/6.64 inference(quant_intro,[status(thm)],[206])).
% 6.45/6.64 tff(208,plain,
% 6.45/6.64 (^[Event: $i, Fluent: $i, Time: $i] : rewrite((initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time)))) <=> (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning)))))))),
% 6.45/6.64 inference(bind,[status(th)],[])).
% 6.45/6.64 tff(209,plain,
% 6.45/6.64 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time)))) <=> ![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))),
% 6.45/6.64 inference(quant_intro,[status(thm)],[208])).
% 6.45/6.64 tff(210,plain,
% 6.45/6.64 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time)))) <=> ![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time))))),
% 6.45/6.64 inference(rewrite,[status(thm)],[])).
% 6.45/6.64 tff(211,plain,
% 6.45/6.64 (^[Event: $i, Fluent: $i, Time: $i] : rewrite((initiates(Event, Fluent, Time) <=> (((((Event = push) & (Fluent = forwards)) & (~happens(pull, Time))) | (((Event = pull) & (Fluent = backwards)) & (~happens(push, Time)))) | (((Event = pull) & (Fluent = spinning)) & happens(push, Time)))) <=> (initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time)))))),
% 6.45/6.64 inference(bind,[status(th)],[])).
% 6.45/6.64 tff(212,plain,
% 6.45/6.64 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((((Event = push) & (Fluent = forwards)) & (~happens(pull, Time))) | (((Event = pull) & (Fluent = backwards)) & (~happens(push, Time)))) | (((Event = pull) & (Fluent = spinning)) & happens(push, Time)))) <=> ![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time))))),
% 6.45/6.64 inference(quant_intro,[status(thm)],[211])).
% 6.45/6.64 tff(213,axiom,(![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((((Event = push) & (Fluent = forwards)) & (~happens(pull, Time))) | (((Event = pull) & (Fluent = backwards)) & (~happens(push, Time)))) | (((Event = pull) & (Fluent = spinning)) & happens(push, Time))))), file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax','initiates_all_defn')).
% 6.45/6.64 tff(214,plain,
% 6.45/6.64 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time))))),
% 6.45/6.64 inference(modus_ponens,[status(thm)],[213, 212])).
% 6.45/6.64 tff(215,plain,
% 6.45/6.64 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time))))),
% 6.45/6.64 inference(modus_ponens,[status(thm)],[214, 210])).
% 6.45/6.64 tff(216,plain,(
% 6.45/6.64 ![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> (((Event = push) & (Fluent = forwards) & (~happens(pull, Time))) | ((Event = pull) & (Fluent = backwards) & (~happens(push, Time))) | ((Event = pull) & (Fluent = spinning) & happens(push, Time))))),
% 6.45/6.64 inference(skolemize,[status(sab)],[215])).
% 6.45/6.64 tff(217,plain,
% 6.45/6.64 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))),
% 6.45/6.64 inference(modus_ponens,[status(thm)],[216, 209])).
% 6.45/6.64 tff(218,plain,
% 6.45/6.64 (![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))),
% 6.45/6.64 inference(modus_ponens,[status(thm)],[217, 207])).
% 6.45/6.64 tff(219,plain,
% 6.45/6.64 (((~![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (initiates(push, forwards, n0) <=> ((~happens(pull, n0)) | (~((~(push = pull)) | (~(forwards = backwards)) | happens(push, n0))) | (~((~(push = pull)) | (~(forwards = spinning)) | (~happens(push, n0))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (initiates(push, forwards, n0) <=> ((~happens(pull, n0)) | (~((~(push = pull)) | (~(forwards = backwards)) | happens(push, n0))) | (~((~(push = pull)) | (~(forwards = spinning)) | (~happens(push, n0)))))))),
% 6.45/6.64 inference(rewrite,[status(thm)],[])).
% 6.45/6.64 tff(220,plain,
% 6.45/6.64 ((initiates(push, forwards, n0) <=> ((~(happens(pull, n0) | (~(push = push)) | (~(forwards = forwards)))) | (~(happens(push, n0) | (~(push = pull)) | (~(forwards = backwards)))) | (~((~happens(push, n0)) | (~(push = pull)) | (~(forwards = spinning)))))) <=> (initiates(push, forwards, n0) <=> ((~happens(pull, n0)) | (~((~(push = pull)) | (~(forwards = backwards)) | happens(push, n0))) | (~((~(push = pull)) | (~(forwards = spinning)) | (~happens(push, n0))))))),
% 6.45/6.64 inference(rewrite,[status(thm)],[])).
% 6.45/6.64 tff(221,plain,
% 6.45/6.64 (((~![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (initiates(push, forwards, n0) <=> ((~(happens(pull, n0) | (~(push = push)) | (~(forwards = forwards)))) | (~(happens(push, n0) | (~(push = pull)) | (~(forwards = backwards)))) | (~((~happens(push, n0)) | (~(push = pull)) | (~(forwards = spinning))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (initiates(push, forwards, n0) <=> ((~happens(pull, n0)) | (~((~(push = pull)) | (~(forwards = backwards)) | happens(push, n0))) | (~((~(push = pull)) | (~(forwards = spinning)) | (~happens(push, n0)))))))),
% 6.45/6.64 inference(monotonicity,[status(thm)],[220])).
% 6.45/6.64 tff(222,plain,
% 6.45/6.64 (((~![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (initiates(push, forwards, n0) <=> ((~(happens(pull, n0) | (~(push = push)) | (~(forwards = forwards)))) | (~(happens(push, n0) | (~(push = pull)) | (~(forwards = backwards)))) | (~((~happens(push, n0)) | (~(push = pull)) | (~(forwards = spinning))))))) <=> ((~![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (initiates(push, forwards, n0) <=> ((~happens(pull, n0)) | (~((~(push = pull)) | (~(forwards = backwards)) | happens(push, n0))) | (~((~(push = pull)) | (~(forwards = spinning)) | (~happens(push, n0)))))))),
% 6.45/6.64 inference(transitivity,[status(thm)],[221, 219])).
% 6.45/6.64 tff(223,plain,
% 6.45/6.64 ((~![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (initiates(push, forwards, n0) <=> ((~(happens(pull, n0) | (~(push = push)) | (~(forwards = forwards)))) | (~(happens(push, n0) | (~(push = pull)) | (~(forwards = backwards)))) | (~((~happens(push, n0)) | (~(push = pull)) | (~(forwards = spinning))))))),
% 6.45/6.64 inference(quant_inst,[status(thm)],[])).
% 6.45/6.64 tff(224,plain,
% 6.45/6.64 ((~![Event: $i, Fluent: $i, Time: $i] : (initiates(Event, Fluent, Time) <=> ((~(happens(pull, Time) | (~(Event = push)) | (~(Fluent = forwards)))) | (~(happens(push, Time) | (~(Event = pull)) | (~(Fluent = backwards)))) | (~((~happens(push, Time)) | (~(Event = pull)) | (~(Fluent = spinning))))))) | (initiates(push, forwards, n0) <=> ((~happens(pull, n0)) | (~((~(push = pull)) | (~(forwards = backwards)) | happens(push, n0))) | (~((~(push = pull)) | (~(forwards = spinning)) | (~happens(push, n0))))))),
% 6.45/6.64 inference(modus_ponens,[status(thm)],[223, 222])).
% 6.45/6.64 tff(225,plain,
% 6.45/6.64 ($false),
% 6.45/6.64 inference(unit_resolution,[status(thm)],[224, 218, 205])).
% 6.45/6.64 % SZS output end Proof
% 6.45/6.65 % E exiting
%------------------------------------------------------------------------------