%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL109-6 : 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 : n003.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 04:39:26 PM UTC 2026
% Result : Unsatisfiable 1.96s 1.95s
% Output : CNFRefutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of clauses : 63 ( 63 unt; 0 nHn; 6 RR)
% Number of literals : 63 ( 62 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 103 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_7,axiom,
xor(X1,xor(truth,X2)) = xor(xor(X1,truth),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_7) ).
cnf(axiom_1,axiom,
not(X1) = xor(X1,truth),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_1) ).
cnf(implies_definition,axiom,
implies(X1,X2) = xor(truth,and_star(X1,xor(truth,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
cnf(axiom_2,axiom,
xor(X1,falsehood) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_2) ).
cnf(axiom_4,axiom,
and_star(X1,truth) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_4) ).
cnf(false_definition,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_definition) ).
cnf(xor_commutativity,axiom,
xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutativity) ).
cnf(and_star_commutativity,axiom,
and_star(X1,X2) = and_star(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_commutativity) ).
cnf(axiom_8,axiom,
and_star(xor(and_star(xor(truth,X1),X2),truth),X2) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_8) ).
cnf(axiom_6,axiom,
and_star(xor(truth,X1),X1) = falsehood,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_6) ).
cnf(and_star_associativity,axiom,
and_star(and_star(X1,X2),X3) = and_star(X1,and_star(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_associativity) ).
cnf(axiom_5,axiom,
and_star(X1,falsehood) = falsehood,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_5) ).
cnf(prove_wajsberg_mv_4,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_mv_4) ).
cnf(c_0_13,axiom,
xor(X1,xor(truth,X2)) = xor(xor(X1,truth),X2),
axiom_7 ).
cnf(c_0_14,axiom,
not(X1) = xor(X1,truth),
axiom_1 ).
cnf(c_0_15,axiom,
implies(X1,X2) = xor(truth,and_star(X1,xor(truth,X2))),
implies_definition ).
cnf(c_0_16,axiom,
xor(X1,falsehood) = X1,
axiom_2 ).
cnf(c_0_17,axiom,
and_star(X1,truth) = X1,
axiom_4 ).
cnf(c_0_18,plain,
xor(X1,xor(truth,X2)) = xor(not(X1),X2),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,axiom,
not(truth) = falsehood,
false_definition ).
cnf(c_0_20,plain,
xor(truth,X1) = implies(X1,falsehood),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_21,axiom,
xor(X1,X2) = xor(X2,X1),
xor_commutativity ).
cnf(c_0_22,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_14]),c_0_19]),c_0_16]),c_0_14]) ).
cnf(c_0_23,plain,
not(X1) = implies(X1,falsehood),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_14]) ).
cnf(c_0_24,plain,
implies(implies(X1,falsehood),falsehood) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]) ).
cnf(c_0_25,plain,
implies(and_star(X1,implies(X2,falsehood)),falsehood) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_20]),c_0_20]) ).
cnf(c_0_26,plain,
and_star(X1,implies(X2,falsehood)) = implies(implies(X1,X2),falsehood),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,axiom,
and_star(X1,X2) = and_star(X2,X1),
and_star_commutativity ).
cnf(c_0_28,plain,
and_star(X1,X2) = implies(implies(X1,implies(X2,falsehood)),falsehood),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_29,axiom,
and_star(xor(and_star(xor(truth,X1),X2),truth),X2) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1),
axiom_8 ).
cnf(c_0_30,plain,
implies(implies(X1,implies(X2,falsehood)),falsehood) = implies(implies(X2,implies(X1,falsehood)),falsehood),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_28]) ).
cnf(c_0_31,plain,
and_star(X1,not(and_star(xor(truth,X2),X1))) = and_star(X2,not(and_star(xor(truth,X1),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_14]),c_0_27]),c_0_14]),c_0_27]) ).
cnf(c_0_32,plain,
implies(X1,implies(X2,falsehood)) = implies(X2,implies(X1,falsehood)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_30]),c_0_24]) ).
cnf(c_0_33,axiom,
and_star(xor(truth,X1),X1) = falsehood,
axiom_6 ).
cnf(c_0_34,plain,
and_star(X1,implies(and_star(implies(X2,falsehood),X1),falsehood)) = and_star(X2,implies(and_star(implies(X1,falsehood),X2),falsehood)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_20]),c_0_23]),c_0_20]),c_0_23]) ).
cnf(c_0_35,plain,
implies(implies(X1,falsehood),implies(X2,falsehood)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_36,axiom,
and_star(and_star(X1,X2),X3) = and_star(X1,and_star(X2,X3)),
and_star_associativity ).
cnf(c_0_37,plain,
and_star(X1,xor(truth,X1)) = falsehood,
inference(rw,[status(thm)],[c_0_33,c_0_27]) ).
cnf(c_0_38,axiom,
and_star(X1,falsehood) = falsehood,
axiom_5 ).
cnf(c_0_39,plain,
and_star(truth,X1) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_27]) ).
cnf(c_0_40,plain,
implies(implies(X1,implies(implies(X1,X2),falsehood)),falsehood) = implies(implies(X2,implies(implies(X2,X1),falsehood)),falsehood),
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_34,c_0_26]),c_0_26]),c_0_28]),c_0_35]),c_0_28]),c_0_35]) ).
cnf(c_0_41,plain,
implies(implies(X1,implies(X2,implies(X3,falsehood))),falsehood) = implies(implies(X2,implies(X3,implies(X1,falsehood))),falsehood),
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_36,c_0_28]),c_0_28]),c_0_28]),c_0_28]),c_0_24]),c_0_35]) ).
cnf(c_0_42,plain,
implies(X1,X1) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_37]),c_0_16]) ).
cnf(c_0_43,plain,
implies(X1,truth) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_14]),c_0_19]),c_0_38]),c_0_16]) ).
cnf(c_0_44,plain,
implies(truth,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_39]),c_0_24]) ).
cnf(c_0_45,plain,
implies(X1,implies(implies(X1,X2),falsehood)) = implies(X2,implies(implies(X2,X1),falsehood)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_40]),c_0_24]) ).
cnf(c_0_46,plain,
implies(implies(X1,implies(X2,X1)),falsehood) = falsehood,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_24]),c_0_43]),c_0_44]) ).
cnf(c_0_47,plain,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_35]),c_0_35]),c_0_35]),c_0_35]) ).
cnf(c_0_48,plain,
implies(X1,implies(X2,X1)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_46]),c_0_42]) ).
cnf(c_0_49,plain,
implies(X1,implies(X2,implies(X3,falsehood))) = implies(X2,implies(X3,implies(X1,falsehood))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_41]),c_0_24]) ).
cnf(c_0_50,plain,
implies(implies(X1,falsehood),X2) = implies(implies(X2,falsehood),X1),
inference(spm,[status(thm)],[c_0_35,c_0_24]) ).
cnf(c_0_51,plain,
implies(implies(implies(X1,X2),X2),X2) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_44]) ).
cnf(c_0_52,plain,
implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_24]),c_0_24]) ).
cnf(c_0_53,plain,
implies(implies(implies(X1,X2),X2),X1) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_51,c_0_47]) ).
cnf(c_0_54,plain,
implies(X1,implies(implies(X1,X2),X2)) = truth,
inference(spm,[status(thm)],[c_0_48,c_0_47]) ).
cnf(c_0_55,plain,
implies(implies(implies(X1,X2),falsehood),X3) = implies(X1,implies(implies(X3,falsehood),X2)),
inference(spm,[status(thm)],[c_0_50,c_0_52]) ).
cnf(c_0_56,plain,
implies(implies(X1,X2),implies(implies(implies(X2,X1),X1),falsehood)) = implies(X2,falsehood),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_53]),c_0_54]),c_0_44]),c_0_32]) ).
cnf(c_0_57,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
prove_wajsberg_mv_4 ).
cnf(c_0_58,plain,
implies(implies(implies(X1,X2),X2),implies(X3,X1)) = implies(X3,implies(X2,X1)),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,plain,
implies(implies(X1,X2),implies(implies(implies(X2,X1),X1),X3)) = implies(X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_24]),c_0_35]) ).
cnf(c_0_60,negated_conjecture,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_52]),c_0_52]) ).
cnf(c_0_61,plain,
implies(X1,implies(implies(X2,X1),X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_48]),c_0_44]),c_0_52]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61]),c_0_47]),c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LCL109-6 : TPTP v9.2.1. Released v1.0.0.
% 0.12/0.13 % 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
% 0.16/0.34 % Computer : n003.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 21:59:41 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.96/1.95 % Version : CSE_E---1.7
% 1.96/1.95 % Problem : theBenchmark.p
% 1.96/1.95 % SZS status Unsatisfiable for theBenchmark.p
% 1.96/1.95 % SZS output start CNFRefutation
% See solution above
% 1.96/1.96 % Total time : 1.375s
%------------------------------------------------------------------------------