%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV041+1 : TPTP v9.2.1. Bugfixed v3.3.0.
% 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 05:20:41 PM UTC 2026
% Result : Theorem 1.35s 1.75s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 13 unt; 0 def)
% Number of atoms : 59 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 49 ( 16 ~; 10 |; 14 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(leq_gt_pred,axiom,
! [X1,X2] :
( leq(X1,pred(X2))
<=> gt(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt_pred) ).
fof(pred_minus_1,axiom,
! [X1] : minus(X1,n1) = pred(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
fof(gauss_init_0077,conjecture,
( ( geq(minus(n330,n1),n0)
& geq(minus(n410,n1),n0) )
=> ! [X14] :
( ( leq(n0,X14)
& leq(X14,n2) )
=> ! [X18] :
( ( leq(n0,X18)
& leq(X18,minus(n0,n1)) )
=> a_select3(tptp_const_array2(dim(n0,n3),dim(n0,n2),uninit),X18,X14) = init ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gauss_init_0077) ).
fof(leq_gt1,axiom,
! [X1,X2] :
( gt(X2,X1)
=> leq(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt1) ).
fof(finite_domain_0,axiom,
! [X1] :
( ( leq(n0,X1)
& leq(X1,n0) )
=> X1 = n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
fof(irreflexivity_gt,axiom,
! [X1] : ~ gt(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',irreflexivity_gt) ).
fof(c_0_6,plain,
! [X216,X217] :
( ( ~ leq(X216,pred(X217))
| gt(X217,X216) )
& ( ~ gt(X217,X216)
| leq(X216,pred(X217)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_gt_pred])]) ).
fof(c_0_7,plain,
! [X315] : minus(X315,n1) = pred(X315),
inference(variable_rename,[status(thm)],[pred_minus_1]) ).
fof(c_0_8,negated_conjecture,
~ ( ( geq(minus(n330,n1),n0)
& geq(minus(n410,n1),n0) )
=> ! [X14] :
( ( leq(n0,X14)
& leq(X14,n2) )
=> ! [X18] :
( ( leq(n0,X18)
& leq(X18,minus(n0,n1)) )
=> a_select3(tptp_const_array2(dim(n0,n3),dim(n0,n2),uninit),X18,X14) = init ) ) ),
inference(assume_negation,[status(cth)],[gauss_init_0077]) ).
cnf(c_0_9,plain,
( gt(X2,X1)
| ~ leq(X1,pred(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
minus(X1,n1) = pred(X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
( geq(minus(n330,n1),n0)
& geq(minus(n410,n1),n0)
& leq(n0,esk24_0)
& leq(esk24_0,n2)
& leq(n0,esk25_0)
& leq(esk25_0,minus(n0,n1))
& a_select3(tptp_const_array2(dim(n0,n3),dim(n0,n2),uninit),esk25_0,esk24_0) != init ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X212,X213] :
( ~ gt(X213,X212)
| leq(X212,X213) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_gt1])]) ).
cnf(c_0_13,plain,
( gt(X2,X1)
| ~ leq(X1,minus(X2,n1)) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
leq(esk25_0,minus(n0,n1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X360] :
( ~ leq(n0,X360)
| ~ leq(X360,n0)
| X360 = n0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[finite_domain_0])]) ).
cnf(c_0_16,plain,
( leq(X2,X1)
| ~ gt(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
gt(n0,esk25_0),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_18,plain,
! [X1] : ~ gt(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_gt]) ).
cnf(c_0_19,plain,
( X1 = n0
| ~ leq(n0,X1)
| ~ leq(X1,n0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
leq(esk25_0,n0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
leq(n0,esk25_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_22,plain,
! [X203] : ~ gt(X203,X203),
inference(variable_rename,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
esk25_0 = n0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_24,plain,
~ gt(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_23]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV041+1 : TPTP v9.2.1. Bugfixed v3.3.0.
% 0.12/0.13 % 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
% 0.16/0.34 % Computer : n001.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 04:54:48 EDT 2026
% 0.16/0.35 % CPUTime :
% 0.20/0.36 % start to proof: theBenchmark
% 1.35/1.75 % Version : CSE_E---1.7
% 1.35/1.75 % Problem : theBenchmark.p
% 1.35/1.75 % SZS status Theorem for theBenchmark.p
% 1.35/1.75 % SZS output start CNFRefutation
% See solution above
% 1.35/1.75 % Total time : 1.378s
%------------------------------------------------------------------------------