%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL160-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n002.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 : Tue May 5 04:39:33 PM UTC 2026
% Result : Unsatisfiable 140.61s 102.02s
% Output : CNFRefutation 141.84s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_18)
% Comments :
%------------------------------------------------------------------------------
cnf(and_star_definition,axiom,
and_star(X1,X2) = not(or(not(X1),not(X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',and_star_definition) ).
cnf(or_definition,axiom,
or(X1,X2) = implies(not(X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',or_definition) ).
cnf(and_definition,axiom,
and(X1,X2) = not(or(not(X1),not(X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',and_definition) ).
cnf(prove_alternative_wajsberg_axiom,negated_conjecture,
and_star(xor(and_star(xor(truth,x),y),truth),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(and_star_associativity,axiom,
and_star(and_star(X1,X2),X3) = and_star(X1,and_star(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',and_star_associativity) ).
cnf(and_associativity,axiom,
and(and(X1,X2),X3) = and(X1,and(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',and_associativity) ).
cnf(xor_definition,axiom,
xor(X1,X2) = or(and(X1,not(X2)),and(not(X1),X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',xor_definition) ).
cnf(and_star_commutativity,axiom,
and_star(X1,X2) = and_star(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',and_star_commutativity) ).
cnf(and_commutativity,axiom,
and(X1,X2) = and(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',and_commutativity) ).
cnf(or_associativity,axiom,
or(or(X1,X2),X3) = or(X1,or(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',or_associativity) ).
cnf(or_commutativity,axiom,
or(X1,X2) = or(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',or_commutativity) ).
cnf(wajsberg_2,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_4) ).
cnf(wajsberg_3,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
cnf(xor_commutativity,axiom,
xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',xor_commutativity) ).
cnf(wajsberg_1,axiom,
implies(truth,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
cnf(false_definition,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',false_definition) ).
cnf(i_0_17,axiom,
and_star(X1,X2) = not(or(not(X1),not(X2))),
and_star_definition ).
cnf(i_0_18,axiom,
or(X1,X2) = implies(not(X1),X2),
or_definition ).
cnf(i_0_19,axiom,
and(X1,X2) = not(or(not(X1),not(X2))),
and_definition ).
cnf(i_0_20,negated_conjecture,
and_star(xor(and_star(xor(truth,x),y),truth),y) != and_star(xor(and_star(xor(truth,y),x),truth),x),
prove_alternative_wajsberg_axiom ).
cnf(i_0_21,plain,
and_star(X1,X2) = not(implies(not(not(X1)),not(X2))),
inference(rw,[status(thm)],[i_0_17,c_0_18]) ).
cnf(i_0_22,axiom,
and_star(and_star(X1,X2),X3) = and_star(X1,and_star(X2,X3)),
and_star_associativity ).
cnf(i_0_23,axiom,
and(and(X1,X2),X3) = and(X1,and(X2,X3)),
and_associativity ).
cnf(i_0_24,plain,
and(X1,X2) = not(implies(not(not(X1)),not(X2))),
inference(rw,[status(thm)],[i_0_19,c_0_18]) ).
cnf(i_0_25,axiom,
xor(X1,X2) = or(and(X1,not(X2)),and(not(X1),X2)),
xor_definition ).
cnf(i_0_26,axiom,
and_star(X1,X2) = and_star(X2,X1),
and_star_commutativity ).
cnf(i_0_27,axiom,
and(X1,X2) = and(X2,X1),
and_commutativity ).
cnf(i_0_28,axiom,
or(or(X1,X2),X3) = or(X1,or(X2,X3)),
or_associativity ).
cnf(i_0_29,axiom,
or(X1,X2) = or(X2,X1),
or_commutativity ).
cnf(i_0_30,negated_conjecture,
not(implies(not(not(xor(not(implies(not(not(xor(truth,y))),not(x))),truth))),not(x))) != not(implies(not(not(xor(not(implies(not(not(xor(truth,x))),not(y))),truth))),not(y))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_20,c_0_21]),c_0_21]),c_0_21]),c_0_21]),
[final] ).
cnf(i_0_31,plain,
not(implies(not(not(not(implies(not(not(X1)),not(X2))))),not(X3))) = not(implies(not(not(X1)),not(not(implies(not(not(X2)),not(X3)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_22,c_0_21]),c_0_21]),c_0_21]),c_0_21]),
[final] ).
cnf(i_0_32,plain,
not(implies(not(not(not(implies(not(not(X1)),not(X2))))),not(X3))) = not(implies(not(not(X1)),not(not(implies(not(not(X2)),not(X3)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_23,c_0_24]),c_0_24]),c_0_24]),c_0_24]),
[final] ).
cnf(i_0_33,plain,
xor(X1,X2) = implies(not(not(implies(not(not(X1)),not(not(X2))))),not(implies(not(not(not(X1))),not(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_25,c_0_18]),c_0_24]),c_0_24]),
[final] ).
cnf(i_0_34,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
wajsberg_2,
[final] ).
cnf(i_0_35,plain,
not(implies(not(not(X1)),not(X2))) = not(implies(not(not(X2)),not(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_26,c_0_21]),c_0_21]),
[final] ).
cnf(i_0_36,plain,
not(implies(not(not(X1)),not(X2))) = not(implies(not(not(X2)),not(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_27,c_0_24]),c_0_24]),
[final] ).
cnf(i_0_37,plain,
implies(not(implies(not(X1),X2)),X3) = implies(not(X1),implies(not(X2),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_28,c_0_18]),c_0_18]),c_0_18]),c_0_18]),
[final] ).
cnf(i_0_38,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
wajsberg_4,
[final] ).
cnf(i_0_39,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
wajsberg_3,
[final] ).
cnf(i_0_40,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_29,c_0_18]),c_0_18]),
[final] ).
cnf(i_0_41,axiom,
xor(X1,X2) = xor(X2,X1),
xor_commutativity,
[final] ).
cnf(i_0_42,axiom,
implies(truth,X1) = X1,
wajsberg_1,
[final] ).
cnf(i_0_43,axiom,
not(truth) = falsehood,
false_definition,
[final] ).
cnf(i_0_44,axiom,
X1 = X1 ).
cnf(i_0_45,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_46,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_47,axiom,
( X1 != X2
| not(X1) = not(X2) ) ).
cnf(i_0_48,axiom,
( X1 != X2
| implies(X1,X3) = implies(X2,X3) ) ).
cnf(i_0_49,axiom,
( X1 != X2
| implies(X3,X1) = implies(X3,X2) ) ).
cnf(i_0_50,axiom,
( X1 != X2
| xor(X1,X3) = xor(X2,X3) ) ).
cnf(i_0_51,axiom,
( X1 != X2
| xor(X3,X1) = xor(X3,X2) ) ).
cnf(i_0_52,plain,
X1 = implies(truth,X1),
inference(scs_inference,[],[i_0_42,i_0_45]) ).
cnf(i_0_55,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_56,plain,
falsehood = not(truth),
inference(scs_inference,[],[i_0_43,i_0_45]) ).
cnf(i_0_61,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_65,plain,
truth = implies(implies(not(X1),not(X2)),implies(X2,X1)),
inference(scs_inference,[],[i_0_38,i_0_45]) ).
cnf(i_0_75,plain,
implies(not(X1),implies(not(X2),X3)) = implies(not(implies(not(X1),X2)),X3),
inference(scs_inference,[],[i_0_37,i_0_45]) ).
cnf(i_0_77,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_125,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_151,plain,
not(implies(not(not(X1)),not(X2))) = not(implies(not(not(X2)),not(X1))),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_320,plain,
not(implies(not(not(X1)),not(X2))) = not(implies(not(not(X2)),not(X1))),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_326,plain,
not(implies(not(not(X1)),not(X2))) = not(implies(not(not(X2)),not(X1))),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_344,plain,
implies(not(implies(not(X1),X2)),X3) = implies(not(X1),implies(not(X2),X3)),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_351,plain,
implies(not(implies(not(X1),X2)),X3) = implies(not(X1),implies(not(X2),X3)),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_355,plain,
implies(not(implies(not(X1),X2)),X3) = implies(not(X1),implies(not(X2),X3)),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_392,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_396,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_398,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_401,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_405,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_408,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_418,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_420,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_422,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_425,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_429,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_433,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_444,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_448,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_452,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_467,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_472,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_476,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_478,plain,
implies(not(X1),implies(not(X2),X3)) = implies(not(X2),implies(not(X3),X1)),
inference(scs_inference,[],[i_0_40,i_0_37,i_0_46]) ).
cnf(i_0_479,plain,
implies(not(implies(not(X1),X2)),X3) = implies(not(X1),implies(not(X2),X3)),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_480,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_481,plain,
implies(not(X1),implies(not(X2),X3)) = implies(not(X3),implies(not(X1),X2)),
inference(scs_inference,[],[i_0_40,i_0_37,i_0_46,i_0_45]) ).
cnf(i_0_672,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_675,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_678,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_681,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_684,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_687,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_690,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_693,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_696,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_699,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_702,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_705,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_708,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_711,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_714,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_717,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_720,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_723,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_726,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_729,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_732,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_735,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_738,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_741,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_744,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_747,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_750,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_753,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_756,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_759,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_762,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_765,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_768,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_771,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_774,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_777,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_780,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_783,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_786,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_789,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_792,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_795,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_798,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_801,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_804,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_807,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_810,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_813,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_816,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_819,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_822,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_825,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_828,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_831,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_834,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_837,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_840,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_843,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_846,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_849,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_852,plain,
implies(truth,X1) = X1,
inference(rename_variables,[],[i_0_42]) ).
cnf(c_0_86,plain,
truth = implies(implies(not(X1),not(X2)),implies(X2,X1)),
i_0_65 ).
cnf(c_0_87,plain,
X1 = implies(truth,X1),
i_0_52 ).
cnf(c_0_88,plain,
falsehood = not(truth),
i_0_56 ).
cnf(c_0_89,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
i_0_39 ).
cnf(c_0_90,plain,
implies(implies(not(X1),falsehood),X1) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]) ).
cnf(c_0_91,plain,
implies(not(X1),X2) = implies(not(X2),X1),
i_0_40 ).
cnf(c_0_92,plain,
implies(implies(X1,truth),truth) = implies(X1,X1),
inference(spm,[status(thm)],[c_0_89,c_0_87]) ).
cnf(c_0_93,plain,
implies(implies(not(falsehood),X1),X1) = truth,
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_94,plain,
implies(not(X1),not(X1)) = implies(implies(falsehood,X1),truth),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_91]),c_0_88]) ).
cnf(c_0_95,plain,
implies(implies(falsehood,falsehood),truth) = truth,
inference(spm,[status(thm)],[c_0_90,c_0_88]) ).
cnf(c_0_96,plain,
not(falsehood) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]),c_0_87]) ).
cnf(c_0_97,plain,
implies(X1,X1) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_96]),c_0_87]) ).
cnf(c_0_98,plain,
implies(not(X1),implies(not(X2),X3)) = implies(not(implies(not(X1),X2)),X3),
i_0_75 ).
cnf(c_0_99,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
i_0_34 ).
cnf(c_0_100,plain,
implies(implies(falsehood,X1),truth) = truth,
inference(rw,[status(thm)],[c_0_94,c_0_97]) ).
cnf(c_0_101,plain,
implies(implies(X1,truth),truth) = truth,
inference(rw,[status(thm)],[c_0_92,c_0_97]) ).
cnf(c_0_102,plain,
implies(not(X1),implies(not(not(X1)),X2)) = implies(falsehood,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_97]),c_0_88]) ).
cnf(c_0_103,plain,
implies(not(X1),truth) = implies(falsehood,X1),
inference(spm,[status(thm)],[c_0_91,c_0_88]) ).
cnf(c_0_104,plain,
implies(implies(implies(falsehood,X1),X2),truth) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]) ).
cnf(c_0_105,plain,
implies(falsehood,not(not(X1))) = implies(falsehood,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_97]),c_0_103]) ).
cnf(c_0_106,plain,
implies(not(X1),falsehood) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_96]),c_0_87]) ).
cnf(c_0_107,plain,
implies(X1,truth) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_97]),c_0_87]) ).
cnf(c_0_108,plain,
implies(implies(falsehood,X1),not(not(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_105]),c_0_106]),c_0_106]) ).
cnf(c_0_109,plain,
implies(falsehood,X1) = truth,
inference(rw,[status(thm)],[c_0_103,c_0_107]) ).
cnf(c_0_110,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109]),c_0_87]) ).
cnf(c_0_111,plain,
xor(X1,X2) = implies(not(not(implies(not(not(X1)),not(not(X2))))),not(implies(not(not(not(X1))),not(X2)))),
i_0_33 ).
cnf(c_0_112,plain,
implies(not(X1),not(X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_91,c_0_110]) ).
cnf(c_0_113,plain,
implies(implies(X1,X2),not(implies(X2,X1))) = xor(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_110]),c_0_110]),c_0_110]),c_0_110]),c_0_112]) ).
cnf(c_0_114,plain,
not(X1) = xor(X1,truth),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_87]),c_0_107]),c_0_87]) ).
cnf(c_0_115,plain,
implies(xor(X1,truth),xor(X2,truth)) = implies(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_114]),c_0_114]) ).
cnf(c_0_116,axiom,
xor(X1,X2) = xor(X2,X1),
i_0_41 ).
cnf(c_0_117,plain,
implies(xor(X1,truth),xor(truth,X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_118,plain,
xor(truth,xor(X1,truth)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_114]),c_0_114]),c_0_116]) ).
cnf(c_0_119,plain,
implies(not(implies(X1,X2)),X3) = implies(X1,implies(not(X2),X3)),
inference(spm,[status(thm)],[c_0_98,c_0_110]) ).
cnf(c_0_120,plain,
implies(X1,implies(X2,X1)) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_107]),c_0_87]),c_0_87]) ).
cnf(c_0_121,plain,
implies(xor(truth,X1),xor(truth,X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_117,c_0_116]) ).
cnf(c_0_122,plain,
xor(truth,xor(truth,X1)) = X1,
inference(spm,[status(thm)],[c_0_118,c_0_116]) ).
cnf(c_0_123,plain,
implies(xor(truth,implies(X1,X2)),X3) = implies(X1,implies(xor(X2,truth),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_114]),c_0_116]),c_0_114]) ).
cnf(c_0_124,plain,
implies(xor(truth,X1),xor(X2,truth)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_125,plain,
implies(X1,implies(not(X1),X2)) = truth,
inference(spm,[status(thm)],[c_0_120,c_0_91]) ).
cnf(c_0_126,plain,
implies(X1,xor(truth,X2)) = implies(X2,xor(truth,X1)),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_127,plain,
implies(implies(X1,X2),xor(truth,implies(X2,X1))) = xor(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114]),c_0_116]) ).
cnf(c_0_128,plain,
implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_115]) ).
cnf(c_0_129,plain,
implies(X1,implies(xor(X1,truth),X2)) = truth,
inference(rw,[status(thm)],[c_0_125,c_0_114]) ).
cnf(c_0_130,plain,
xor(truth,truth) = falsehood,
inference(rw,[status(thm)],[c_0_88,c_0_114]) ).
cnf(c_0_131,plain,
implies(X1,falsehood) = not(X1),
inference(spm,[status(thm)],[c_0_106,c_0_110]) ).
cnf(c_0_132,negated_conjecture,
not(implies(not(not(xor(not(implies(not(not(xor(truth,y))),not(x))),truth))),not(x))) != not(implies(not(not(xor(not(implies(not(not(xor(truth,x))),not(y))),truth))),not(y))),
i_0_30 ).
cnf(c_0_133,plain,
implies(implies(X1,implies(xor(X2,truth),X3)),X3) = implies(implies(X1,X2),xor(truth,implies(X3,xor(truth,implies(X1,X2))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_123]),c_0_126]) ).
cnf(c_0_134,plain,
implies(xor(X1,X2),xor(truth,implies(X2,X1))) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_127]),c_0_123]),c_0_128]),c_0_129]),c_0_107]),c_0_87]) ).
cnf(c_0_135,plain,
xor(truth,implies(implies(X1,X2),X2)) = xor(X2,implies(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_120]),c_0_130]),c_0_131]),c_0_114]),c_0_116]),c_0_116]) ).
cnf(c_0_136,negated_conjecture,
not(implies(not(not(y)),not(xor(truth,not(implies(not(not(y)),not(xor(truth,x)))))))) != not(implies(not(not(x)),not(xor(truth,not(implies(not(not(x)),not(xor(truth,y)))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_116]),c_0_116]),c_0_91]),c_0_91]),c_0_91]),c_0_91]) ).
cnf(c_0_137,plain,
implies(implies(X1,X2),implies(implies(X2,X1),X3)) = implies(xor(truth,xor(X1,X2)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_127]),c_0_116]),c_0_122]) ).
cnf(c_0_138,plain,
implies(implies(X1,X2),xor(X2,implies(X1,X2))) = xor(truth,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_107]),c_0_107]),c_0_87]),c_0_87]),c_0_87]),c_0_121]),c_0_135]) ).
cnf(c_0_139,plain,
implies(xor(truth,X1),xor(X2,implies(X3,X2))) = implies(implies(implies(X3,X2),X2),X1),
inference(spm,[status(thm)],[c_0_121,c_0_135]) ).
cnf(c_0_140,negated_conjecture,
not(implies(y,not(xor(truth,not(implies(y,not(xor(truth,x)))))))) != not(implies(x,not(xor(truth,not(implies(x,not(xor(truth,y)))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_110]),c_0_110]),c_0_110]),c_0_110]) ).
cnf(c_0_141,plain,
implies(implies(implies(X1,X2),X2),xor(X2,X1)) = implies(X2,xor(truth,implies(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_139]),c_0_126]) ).
cnf(c_0_142,negated_conjecture,
xor(truth,implies(y,xor(truth,xor(truth,xor(truth,implies(y,xor(truth,xor(truth,x)))))))) != xor(truth,implies(x,xor(truth,xor(truth,xor(truth,implies(x,xor(truth,xor(truth,y)))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_114]),c_0_114]),c_0_114]),c_0_114]),c_0_116]),c_0_116]),c_0_116]),c_0_116]),c_0_114]),c_0_114]),c_0_114]),c_0_114]),c_0_116]),c_0_116]),c_0_116]),c_0_116]) ).
cnf(c_0_143,plain,
implies(implies(implies(X1,X2),X2),xor(X1,X2)) = implies(X2,xor(truth,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_141,c_0_116]) ).
cnf(c_0_144,negated_conjecture,
xor(truth,implies(y,xor(truth,implies(y,x)))) != xor(truth,implies(x,xor(truth,implies(x,y)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_122]),c_0_122]),c_0_122]),c_0_122]) ).
cnf(c_0_145,plain,
implies(X1,xor(truth,implies(X1,X2))) = implies(X2,xor(truth,implies(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_89]),c_0_143]) ).
cnf(c_0_146,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_145])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL160-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.12/0.31 % Computer : n002.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Mon May 4 22:05:01 EDT 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.32 % start to proof: theBenchmark
% 140.61/102.02 % Version : CSE_E---1.7
% 140.61/102.02 % Problem : theBenchmark.p
% 140.61/102.02 % SZS status Unsatisfiable for theBenchmark.p
% 140.61/102.02 % SZS output start CNFRefutation
% See solution above
% 141.84/103.16 % Total time : 101.335s
%------------------------------------------------------------------------------