%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL159-1 : 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 : n010.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 04:39:32 PM UTC 2026
% Result : Unsatisfiable 5.99s 4.55s
% Output : CNFRefutation 5.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of clauses : 86 ( 86 unt; 0 nHn; 7 RR)
% Number of literals : 86 ( 85 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 139 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
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(or_definition,axiom,
or(X1,X2) = implies(not(X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',or_definition) ).
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_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(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(or_commutativity,axiom,
or(X1,X2) = or(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',or_commutativity) ).
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(and_definition,axiom,
and(X1,X2) = not(or(not(X1),not(X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-2.ax',and_definition) ).
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(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(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(prove_alternative_wajsberg_axiom,negated_conjecture,
xor(x,xor(truth,y)) != xor(xor(x,truth),y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(xor_commutativity,axiom,
xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-1.ax',xor_commutativity) ).
cnf(c_0_14,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
wajsberg_4 ).
cnf(c_0_15,axiom,
or(X1,X2) = implies(not(X1),X2),
or_definition ).
cnf(c_0_16,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
wajsberg_2 ).
cnf(c_0_17,axiom,
implies(truth,X1) = X1,
wajsberg_1 ).
cnf(c_0_18,plain,
implies(or(X1,not(X2)),implies(X2,X1)) = truth,
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,axiom,
not(truth) = falsehood,
false_definition ).
cnf(c_0_20,plain,
implies(X1,implies(implies(X1,X2),X2)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_17]) ).
cnf(c_0_21,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
wajsberg_3 ).
cnf(c_0_22,plain,
implies(or(X1,falsehood),X1) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_19]) ).
cnf(c_0_23,axiom,
or(X1,X2) = or(X2,X1),
or_commutativity ).
cnf(c_0_24,plain,
implies(X1,X1) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_20]),c_0_17]) ).
cnf(c_0_25,axiom,
and_star(X1,X2) = not(or(not(X1),not(X2))),
and_star_definition ).
cnf(c_0_26,axiom,
and(X1,X2) = not(or(not(X1),not(X2))),
and_definition ).
cnf(c_0_27,plain,
implies(implies(X1,truth),truth) = implies(X1,X1),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_28,plain,
implies(or(falsehood,X1),X1) = truth,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
or(X1,not(X1)) = truth,
inference(spm,[status(thm)],[c_0_15,c_0_24]) ).
cnf(c_0_30,plain,
and(X1,X2) = and_star(X1,X2),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
implies(implies(X1,truth),truth) = truth,
inference(rw,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_32,plain,
not(falsehood) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_17]) ).
cnf(c_0_33,plain,
not(or(not(X1),not(X2))) = and_star(X1,X2),
inference(rw,[status(thm)],[c_0_26,c_0_30]) ).
cnf(c_0_34,plain,
implies(X1,truth) = truth,
inference(spm,[status(thm)],[c_0_20,c_0_31]) ).
cnf(c_0_35,plain,
or(falsehood,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_32]),c_0_17]) ).
cnf(c_0_36,plain,
not(or(falsehood,not(X1))) = and_star(X1,truth),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_19]),c_0_23]) ).
cnf(c_0_37,plain,
or(X1,truth) = truth,
inference(spm,[status(thm)],[c_0_15,c_0_34]) ).
cnf(c_0_38,axiom,
or(or(X1,X2),X3) = or(X1,or(X2,X3)),
or_associativity ).
cnf(c_0_39,plain,
implies(or(not(X1),X2),implies(X1,X2)) = truth,
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_40,plain,
or(X1,falsehood) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_35]) ).
cnf(c_0_41,plain,
not(not(X1)) = and_star(X1,truth),
inference(rw,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_42,plain,
implies(falsehood,X1) = or(truth,X1),
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_43,plain,
or(truth,X1) = truth,
inference(spm,[status(thm)],[c_0_23,c_0_37]) ).
cnf(c_0_44,plain,
or(not(X1),or(not(X2),X3)) = implies(and_star(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_33]),c_0_38]) ).
cnf(c_0_45,plain,
or(X1,implies(X1,falsehood)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_15]) ).
cnf(c_0_46,plain,
implies(X1,and_star(X1,truth)) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_29]),c_0_17]),c_0_41]) ).
cnf(c_0_47,axiom,
and_star(X1,X2) = and_star(X2,X1),
and_star_commutativity ).
cnf(c_0_48,axiom,
xor(X1,X2) = or(and(X1,not(X2)),and(not(X1),X2)),
xor_definition ).
cnf(c_0_49,plain,
implies(falsehood,X1) = truth,
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
implies(and_star(X1,X2),X2) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_37]),c_0_15]),c_0_40]) ).
cnf(c_0_51,plain,
implies(X1,and_star(truth,X1)) = truth,
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
or(and_star(X1,not(X2)),and_star(not(X1),X2)) = xor(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_30]),c_0_30]) ).
cnf(c_0_53,plain,
implies(implies(X1,falsehood),falsehood) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_49]),c_0_17]) ).
cnf(c_0_54,plain,
implies(and_star(X1,X2),X1) = truth,
inference(spm,[status(thm)],[c_0_50,c_0_47]) ).
cnf(c_0_55,plain,
or(falsehood,or(not(X1),X2)) = implies(and_star(X1,truth),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_36]),c_0_38]) ).
cnf(c_0_56,plain,
and_star(truth,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_51]),c_0_17]),c_0_50]),c_0_17]) ).
cnf(c_0_57,plain,
or(and_star(X1,not(X2)),or(and_star(not(X1),X2),X3)) = or(xor(X1,X2),X3),
inference(spm,[status(thm)],[c_0_38,c_0_52]) ).
cnf(c_0_58,plain,
and_star(falsehood,X1) = falsehood,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_17]) ).
cnf(c_0_59,plain,
or(not(X1),X2) = implies(and_star(X1,truth),X2),
inference(rw,[status(thm)],[c_0_55,c_0_35]) ).
cnf(c_0_60,plain,
and_star(X1,truth) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_56]) ).
cnf(c_0_61,plain,
or(X1,or(X2,X3)) = or(X2,or(X3,X1)),
inference(spm,[status(thm)],[c_0_38,c_0_23]) ).
cnf(c_0_62,plain,
or(xor(truth,X1),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_57,c_0_19]),c_0_56]),c_0_58]),c_0_35]),c_0_59]),c_0_60]) ).
cnf(c_0_63,plain,
implies(X1,falsehood) = not(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_15]),c_0_40]) ).
cnf(c_0_64,plain,
or(X1,or(falsehood,not(X2))) = implies(and_star(X2,truth),X1),
inference(spm,[status(thm)],[c_0_55,c_0_61]) ).
cnf(c_0_65,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[c_0_41,c_0_60]) ).
cnf(c_0_66,plain,
not(X1) = xor(truth,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_62]),c_0_63]) ).
cnf(c_0_67,plain,
or(X1,not(X2)) = implies(and_star(X2,truth),X1),
inference(rw,[status(thm)],[c_0_64,c_0_35]) ).
cnf(c_0_68,plain,
xor(truth,xor(truth,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66]),c_0_66]) ).
cnf(c_0_69,plain,
xor(truth,implies(X1,xor(truth,X2))) = and_star(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_67]),c_0_60]),c_0_66]),c_0_66]) ).
cnf(c_0_70,plain,
implies(xor(truth,X1),X2) = or(X1,X2),
inference(rw,[status(thm)],[c_0_15,c_0_66]) ).
cnf(c_0_71,plain,
implies(X1,xor(truth,X2)) = xor(truth,and_star(X2,X1)),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_72,plain,
or(X1,xor(truth,X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_23,c_0_62]) ).
cnf(c_0_73,plain,
xor(truth,and_star(X1,xor(truth,X2))) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_74,plain,
xor(truth,implies(X1,X2)) = and_star(X1,xor(truth,X2)),
inference(spm,[status(thm)],[c_0_68,c_0_73]) ).
cnf(c_0_75,plain,
or(and_star(X1,xor(truth,X2)),or(and_star(xor(truth,X1),X2),X3)) = or(xor(X1,X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_66]),c_0_66]) ).
cnf(c_0_76,plain,
and_star(xor(truth,X1),xor(truth,X2)) = xor(truth,or(X1,X2)),
inference(spm,[status(thm)],[c_0_74,c_0_70]) ).
cnf(c_0_77,plain,
implies(or(X1,X2),or(and_star(X1,X2),X3)) = or(xor(xor(truth,X1),X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_68]),c_0_76]),c_0_62]) ).
cnf(c_0_78,plain,
implies(or(X1,X2),and_star(X1,X2)) = xor(xor(truth,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_40]),c_0_40]) ).
cnf(c_0_79,plain,
implies(or(X1,X2),and_star(X2,X1)) = xor(X1,xor(truth,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_78,c_0_76]),c_0_62]),c_0_71]),c_0_70]),c_0_72]),c_0_68]) ).
cnf(c_0_80,negated_conjecture,
xor(x,xor(truth,y)) != xor(xor(x,truth),y),
prove_alternative_wajsberg_axiom ).
cnf(c_0_81,axiom,
xor(X1,X2) = xor(X2,X1),
xor_commutativity ).
cnf(c_0_82,plain,
xor(xor(truth,X1),X2) = xor(X1,xor(truth,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_47]),c_0_78]) ).
cnf(c_0_83,negated_conjecture,
xor(y,xor(truth,x)) != xor(x,xor(truth,y)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81]),c_0_81]) ).
cnf(c_0_84,plain,
xor(X1,xor(truth,X2)) = xor(X2,xor(truth,X1)),
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(spm,[status(thm)],[c_0_79,c_0_76]),c_0_62]),c_0_71]),c_0_70]),c_0_72]),c_0_78]),c_0_68]),c_0_82]),c_0_82]) ).
cnf(c_0_85,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL159-1 : 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
% 0.15/0.32 % Computer : n010.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 22:04:21 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 5.99/4.55 % Version : CSE_E---1.7
% 5.99/4.55 % Problem : theBenchmark.p
% 5.99/4.55 % SZS status Unsatisfiable for theBenchmark.p
% 5.99/4.55 % SZS output start CNFRefutation
% See solution above
% 5.99/4.57 % Total time : 3.367s
%------------------------------------------------------------------------------