%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM836+1 : TPTP v9.2.1. Released v4.1.0.
% 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 : n028.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 04:58:40 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 16 unt; 0 def)
% Number of atoms : 40 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 20 ~; 9 |; 3 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 7 sgn 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(73, 0), 0)',axiom,
! [X14,X15] : X15 != vplus(X14,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X21,X22,X23] : vplus(vplus(X21,X22),X23) = vplus(X21,vplus(X22,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X16,X17] : vplus(X17,X16) = vplus(X16,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
! [X1,X2] :
( less(X2,X1)
<=> ? [X3] : X1 = vplus(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [X4,X5] :
( greater(X5,X4)
<=> ? [X6] : X5 = vplus(X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof('dis(ex(cond(conseq(131), 0), 1))',conjecture,
( ~ greater(vd203,vd204)
| ~ less(vd203,vd204) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dis(ex(cond(conseq(131), 0), 1))') ).
fof(c_0_6,plain,
! [X104,X105] : X105 != vplus(X104,X105),
inference(variable_rename,[status(thm)],['ass(cond(73, 0), 0)']) ).
fof(c_0_7,plain,
! [X111,X112,X113] : vplus(vplus(X111,X112),X113) = vplus(X111,vplus(X112,X113)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(c_0_8,plain,
X1 != vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X106,X107] : vplus(X107,X106) = vplus(X106,X107),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_0_11,plain,
vplus(X1,vplus(X2,X3)) != X3,
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X75,X76,X78,X79,X80] :
( ( ~ less(X76,X75)
| X75 = vplus(X76,esk1_2(X75,X76)) )
& ( X78 != vplus(X79,X80)
| less(X79,X78) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 12), 1)'])])])])]) ).
cnf(c_0_14,plain,
vplus(X1,vplus(X2,X3)) != X2,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( X2 = vplus(X1,esk1_2(X2,X1))
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,plain,
~ less(vplus(X1,X2),X2),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15])]) ).
fof(c_0_17,plain,
! [X81,X82,X84,X85,X86] :
( ( ~ greater(X82,X81)
| X82 = vplus(X81,esk2_2(X81,X82)) )
& ( X85 != vplus(X84,X86)
| greater(X85,X84) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 11), 1)'])])])])]) ).
fof(c_0_18,negated_conjecture,
~ ( ~ greater(vd203,vd204)
| ~ less(vd203,vd204) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['dis(ex(cond(conseq(131), 0), 1))'])]) ).
cnf(c_0_19,plain,
~ less(vplus(X1,X2),X1),
inference(spm,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_20,plain,
( X1 = vplus(X2,esk2_2(X2,X1))
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_21,negated_conjecture,
( greater(vd203,vd204)
& less(vd203,vd204) ),
inference(fof_nnf,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( ~ less(X1,X2)
| ~ greater(X1,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
less(vd203,vd204),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_24,negated_conjecture,
greater(vd203,vd204),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM836+1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n028.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:15:00 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.374s
%------------------------------------------------------------------------------