%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL109-10 : TPTP v9.2.1. Released v7.5.0.
% 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 : 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 04:39:25 PM UTC 2026
% Result : Unsatisfiable 25.57s 15.37s
% Output : CNFRefutation 25.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 4 RR)
% Number of literals : 32 ( 31 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_3,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).
cnf(lemma_4,axiom,
implies(X1,implies(X2,X1)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_4) ).
cnf(wajsberg_1,axiom,
implies(truth,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_1) ).
cnf(lemma_7,axiom,
implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_7) ).
cnf(lemma_10,axiom,
implies(not(X1),not(X2)) = implies(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_10) ).
cnf(lemma_9,axiom,
not(not(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_9) ).
cnf(lemma_1,axiom,
implies(X1,X1) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1) ).
cnf(lemma_3,axiom,
implies(X1,truth) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_3) ).
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(c_0_9,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
wajsberg_3 ).
cnf(c_0_10,axiom,
implies(X1,implies(X2,X1)) = truth,
lemma_4 ).
cnf(c_0_11,axiom,
implies(truth,X1) = X1,
wajsberg_1 ).
cnf(c_0_12,axiom,
implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
lemma_7 ).
cnf(c_0_13,axiom,
implies(not(X1),not(X2)) = implies(X2,X1),
lemma_10 ).
cnf(c_0_14,plain,
implies(implies(implies(X1,X2),X2),X2) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_15,axiom,
not(not(X1)) = X1,
lemma_9 ).
cnf(c_0_16,plain,
implies(not(X1),implies(X2,not(X3))) = implies(X2,implies(X3,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
implies(implies(implies(X1,X2),X2),X1) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_14,c_0_9]) ).
cnf(c_0_18,plain,
implies(X1,not(X2)) = implies(X2,not(X1)),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_19,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_20,plain,
implies(not(X1),implies(implies(not(X2),X3),X3)) = implies(X2,implies(implies(X3,not(X2)),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_9]),c_0_12]) ).
cnf(c_0_21,plain,
implies(implies(X1,not(implies(X2,not(X1)))),X2) = implies(not(X1),X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
implies(not(implies(X1,X2)),X3) = implies(X1,implies(not(X3),X2)),
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_23,axiom,
implies(X1,X1) = truth,
lemma_1 ).
cnf(c_0_24,axiom,
implies(X1,truth) = truth,
lemma_3 ).
cnf(c_0_25,plain,
implies(X1,implies(not(X2),X3)) = implies(not(X3),implies(X1,X2)),
inference(spm,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_26,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
prove_wajsberg_mv_4 ).
cnf(c_0_27,plain,
implies(X1,implies(X2,not(X3))) = implies(X3,implies(X1,not(X2))),
inference(spm,[status(thm)],[c_0_12,c_0_18]) ).
cnf(c_0_28,plain,
implies(not(X1),implies(implies(X1,not(X2)),X2)) = implies(not(X1),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(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_13]),c_0_23]),c_0_24]),c_0_11]),c_0_25]) ).
cnf(c_0_29,negated_conjecture,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_12]),c_0_12]) ).
cnf(c_0_30,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_27,c_0_28]),c_0_13]),c_0_15]),c_0_13]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_9]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL109-10 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.12 % 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
% 0.15/0.33 % Computer : n003.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 22:00:26 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 25.57/15.37 % Version : CSE_E---1.7
% 25.57/15.37 % Problem : theBenchmark.p
% 25.57/15.37 % SZS status Unsatisfiable for theBenchmark.p
% 25.57/15.37 % SZS output start CNFRefutation
% See solution above
% 25.68/15.48 % Total time : 11.394s
%------------------------------------------------------------------------------