%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL157-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.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 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 51 ( 51 unt; 0 nHn; 7 RR)
% Number of literals : 51 ( 50 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_4,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_4) ).
cnf(or_definition,axiom,
or(X1,X2) = implies(not(X1),X2),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).
cnf(wajsberg_1,axiom,
implies(truth,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
cnf(false_definition,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',false_definition) ).
cnf(wajsberg_3,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
cnf(or_commutativity,axiom,
or(X1,X2) = or(X2,X1),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL002-1.ax',and_star_definition) ).
cnf(and_definition,axiom,
and(X1,X2) = not(or(not(X1),not(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',and_definition) ).
cnf(or_associativity,axiom,
or(or(X1,X2),X3) = or(X1,or(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',or_associativity) ).
cnf(and_star_commutativity,axiom,
and_star(X1,X2) = and_star(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',and_star_commutativity) ).
cnf(prove_alternative_wajsberg_axiom,negated_conjecture,
and_star(x,falsehood) != falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(c_0_12,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
wajsberg_4 ).
cnf(c_0_13,axiom,
or(X1,X2) = implies(not(X1),X2),
or_definition ).
cnf(c_0_14,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
wajsberg_2 ).
cnf(c_0_15,axiom,
implies(truth,X1) = X1,
wajsberg_1 ).
cnf(c_0_16,plain,
implies(or(X1,not(X2)),implies(X2,X1)) = truth,
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,axiom,
not(truth) = falsehood,
false_definition ).
cnf(c_0_18,plain,
implies(X1,implies(implies(X1,X2),X2)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_15]) ).
cnf(c_0_19,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
wajsberg_3 ).
cnf(c_0_20,plain,
implies(or(X1,falsehood),X1) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_15]),c_0_17]) ).
cnf(c_0_21,axiom,
or(X1,X2) = or(X2,X1),
or_commutativity ).
cnf(c_0_22,plain,
implies(X1,X1) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_18]),c_0_15]) ).
cnf(c_0_23,plain,
implies(implies(X1,truth),truth) = implies(X1,X1),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_24,plain,
implies(or(falsehood,X1),X1) = truth,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
or(X1,not(X1)) = truth,
inference(spm,[status(thm)],[c_0_13,c_0_22]) ).
cnf(c_0_26,plain,
implies(implies(X1,truth),truth) = truth,
inference(rw,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_27,axiom,
and_star(X1,X2) = not(or(not(X1),not(X2))),
and_star_definition ).
cnf(c_0_28,axiom,
and(X1,X2) = not(or(not(X1),not(X2))),
and_definition ).
cnf(c_0_29,plain,
not(falsehood) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_15]) ).
cnf(c_0_30,plain,
implies(X1,truth) = truth,
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_31,plain,
and(X1,X2) = and_star(X1,X2),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
or(falsehood,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_29]),c_0_15]) ).
cnf(c_0_33,plain,
or(X1,truth) = truth,
inference(spm,[status(thm)],[c_0_13,c_0_30]) ).
cnf(c_0_34,plain,
not(or(not(X1),not(X2))) = and_star(X1,X2),
inference(rw,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_35,axiom,
or(or(X1,X2),X3) = or(X1,or(X2,X3)),
or_associativity ).
cnf(c_0_36,plain,
implies(or(not(X1),X2),implies(X1,X2)) = truth,
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_37,plain,
or(X1,falsehood) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_32]) ).
cnf(c_0_38,plain,
implies(falsehood,X1) = or(truth,X1),
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_39,plain,
or(truth,X1) = truth,
inference(spm,[status(thm)],[c_0_21,c_0_33]) ).
cnf(c_0_40,plain,
or(not(X1),or(not(X2),X3)) = implies(and_star(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_34]),c_0_35]) ).
cnf(c_0_41,plain,
or(X1,implies(X1,falsehood)) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_13]) ).
cnf(c_0_42,plain,
implies(falsehood,X1) = truth,
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,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_40,c_0_41]),c_0_33]),c_0_13]),c_0_37]) ).
cnf(c_0_44,axiom,
and_star(X1,X2) = and_star(X2,X1),
and_star_commutativity ).
cnf(c_0_45,negated_conjecture,
and_star(x,falsehood) != falsehood,
prove_alternative_wajsberg_axiom ).
cnf(c_0_46,plain,
implies(implies(X1,falsehood),falsehood) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_42]),c_0_15]) ).
cnf(c_0_47,plain,
implies(and_star(X1,X2),X1) = truth,
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
and_star(falsehood,x) != falsehood,
inference(rw,[status(thm)],[c_0_45,c_0_44]) ).
cnf(c_0_49,plain,
and_star(falsehood,X1) = falsehood,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_15]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL157-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n022.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 22:04:36 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------