%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL109-3 : 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 : n027.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 04:39:25 PM UTC 2026
% Result : Unsatisfiable 4.24s 3.20s
% Output : CNFRefutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 7 RR)
% Number of literals : 30 ( 29 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_wajsberg_mv_4,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_mv_4) ).
cnf(lemma_10,axiom,
implies(not(X1),not(X2)) = implies(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_10) ).
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(lemma_9,axiom,
not(not(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_9) ).
cnf(lemma_7,axiom,
implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_7) ).
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(lemma_4,axiom,
implies(X1,implies(X2,X1)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_4) ).
cnf(lemma_8,axiom,
implies(X1,not(truth)) = not(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_8) ).
cnf(wajsberg_1,axiom,
implies(truth,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
cnf(c_0_9,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
prove_wajsberg_mv_4 ).
cnf(c_0_10,axiom,
implies(not(X1),not(X2)) = implies(X2,X1),
lemma_10 ).
cnf(c_0_11,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
wajsberg_3 ).
cnf(c_0_12,negated_conjecture,
implies(not(implies(b,a)),not(implies(implies(a,b),implies(b,a)))) != truth,
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
implies(not(X1),not(implies(X2,X1))) = implies(not(X2),not(implies(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_10]),c_0_10]) ).
cnf(c_0_14,axiom,
not(not(X1)) = X1,
lemma_9 ).
cnf(c_0_15,negated_conjecture,
implies(not(implies(a,b)),not(implies(implies(b,a),implies(a,b)))) != truth,
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
lemma_7 ).
cnf(c_0_17,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_18,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
wajsberg_2 ).
cnf(c_0_19,plain,
implies(X1,not(X2)) = implies(X2,not(X1)),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_20,axiom,
implies(X1,implies(X2,X1)) = truth,
lemma_4 ).
cnf(c_0_21,axiom,
implies(X1,not(truth)) = not(X1),
lemma_8 ).
cnf(c_0_22,negated_conjecture,
implies(not(implies(a,b)),not(implies(a,implies(not(b),not(implies(b,a)))))) != truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_10]) ).
cnf(c_0_23,plain,
implies(not(implies(X1,X2)),X3) = implies(X1,implies(not(X3),X2)),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_24,plain,
implies(implies(not(X1),X2),implies(not(X3),implies(implies(X1,X3),not(implies(X2,not(implies(X3,X1))))))) = truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_13]),c_0_16]),c_0_19]) ).
cnf(c_0_25,plain,
implies(implies(X1,X2),not(implies(not(X1),not(implies(X2,X1))))) = not(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_13,c_0_13]),c_0_14]),c_0_14]),c_0_10]),c_0_20]),c_0_21]) ).
cnf(c_0_26,axiom,
implies(truth,X1) = X1,
wajsberg_1 ).
cnf(c_0_27,negated_conjecture,
implies(a,implies(not(b),not(implies(a,implies(not(b),not(implies(b,a))))))) != truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_14]),c_0_10]) ).
cnf(c_0_28,plain,
implies(X1,implies(not(X2),not(implies(X1,implies(not(X2),not(implies(X2,X1))))))) = truth,
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(spm,[status(thm)],[c_0_24,c_0_25]),c_0_14]),c_0_14]),c_0_10]),c_0_20]),c_0_14]),c_0_26]),c_0_16]),c_0_10]),c_0_16]),c_0_10]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL109-3 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.14/0.33 % Computer : n027.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 22:00:35 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 4.24/3.20 % Version : CSE_E---1.7
% 4.24/3.20 % Problem : theBenchmark.p
% 4.24/3.20 % SZS status Unsatisfiable for theBenchmark.p
% 4.24/3.20 % SZS output start CNFRefutation
% See solution above
% 4.24/3.22 % Total time : 2.373s
%------------------------------------------------------------------------------