%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL109-5 : 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 : n001.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 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 38 ( 26 unt; 0 nHn; 14 RR)
% Number of literals : 50 ( 25 equ; 15 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(lemma_3_1,axiom,
( ordered(X2,implies(X1,X3))
| ~ ordered(X1,implies(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_3_1) ).
cnf(wajsberg_1,axiom,
implies(truth,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
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(lemma_1,axiom,
( ordered(implies(X1,X3),implies(X2,X3))
| ~ ordered(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1) ).
cnf(partial_order_definition2,axiom,
( ordered(X1,X2)
| implies(X1,X2) != truth ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-1.ax',partial_order_definition2) ).
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(partial_order_definition1,axiom,
( implies(X1,X2) = truth
| ~ ordered(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-1.ax',partial_order_definition1) ).
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(prove_mv_4,negated_conjecture,
big_V(implies(x,y),implies(y,x)) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_mv_4) ).
cnf(big_V_definition,axiom,
big_V(X1,X2) = implies(implies(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-1.ax',big_V_definition) ).
cnf(c_0_10,axiom,
( ordered(X2,implies(X1,X3))
| ~ ordered(X1,implies(X2,X3)) ),
lemma_3_1 ).
cnf(c_0_11,axiom,
implies(truth,X1) = X1,
wajsberg_1 ).
cnf(c_0_12,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
wajsberg_4 ).
cnf(c_0_13,plain,
( ordered(truth,implies(X1,X2))
| ~ ordered(X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
implies(implies(not(X1),not(truth)),X1) = truth,
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_15,axiom,
( ordered(implies(X1,X3),implies(X2,X3))
| ~ ordered(X1,X2) ),
lemma_1 ).
cnf(c_0_16,plain,
( ordered(truth,truth)
| ~ ordered(implies(not(X1),not(truth)),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
( ordered(X1,X2)
| implies(X1,X2) != truth ),
partial_order_definition2 ).
cnf(c_0_18,plain,
( ordered(implies(X1,X2),X2)
| ~ ordered(X1,truth) ),
inference(spm,[status(thm)],[c_0_15,c_0_11]) ).
cnf(c_0_19,plain,
ordered(truth,truth),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14])]) ).
cnf(c_0_20,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
wajsberg_3 ).
cnf(c_0_21,axiom,
( implies(X1,X2) = truth
| ~ ordered(X1,X2) ),
partial_order_definition1 ).
cnf(c_0_22,plain,
ordered(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_11]),c_0_19])]) ).
cnf(c_0_23,plain,
implies(implies(X1,truth),truth) = implies(X1,X1),
inference(spm,[status(thm)],[c_0_20,c_0_11]) ).
cnf(c_0_24,plain,
implies(X1,X1) = truth,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
wajsberg_2 ).
cnf(c_0_26,plain,
implies(implies(X1,truth),truth) = truth,
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
implies(implies(implies(X1,truth),X2),truth) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_26]) ).
cnf(c_0_28,plain,
( ordered(X1,implies(X2,X3))
| implies(X2,implies(X1,X3)) != truth ),
inference(spm,[status(thm)],[c_0_10,c_0_17]) ).
cnf(c_0_29,plain,
implies(X1,truth) = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_27]),c_0_11]) ).
cnf(c_0_30,plain,
ordered(X1,truth),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_29]),c_0_29])]) ).
cnf(c_0_31,plain,
ordered(implies(X1,X2),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_30])]) ).
cnf(c_0_32,negated_conjecture,
big_V(implies(x,y),implies(y,x)) != truth,
prove_mv_4 ).
cnf(c_0_33,axiom,
big_V(X1,X2) = implies(implies(X1,X2),X2),
big_V_definition ).
cnf(c_0_34,plain,
ordered(truth,X1),
inference(spm,[status(thm)],[c_0_31,c_0_14]) ).
cnf(c_0_35,negated_conjecture,
implies(implies(implies(x,y),implies(y,x)),implies(y,x)) != truth,
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,plain,
X1 = truth,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_34]),c_0_11]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL109-5 : 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
% 0.15/0.33 % Computer : n001.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 22:00:48 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------