%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV041+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:06:41 AM UTC 2026
% Result : Theorem 10.65s 1.78s
% Output : CNFRefutation 10.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 27 unt; 0 def)
% Number of atoms : 77 ( 23 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 49 ( 13 ~; 8 |; 19 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-3 aty)
% Number of variables : 36 ( 0 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexivity_gt,axiom,
! [X] : ~ gt(X,X),
file('theBenchmark.p',irreflexivity_gt) ).
fof(leq_succ,axiom,
! [X,Y] :
( leq(X,Y)
=> leq(X,succ(Y)) ),
file('theBenchmark.p',leq_succ) ).
fof(leq_succ_gt_equiv,axiom,
! [X,Y] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
file('theBenchmark.p',leq_succ_gt_equiv) ).
fof(succ_plus_1_r,axiom,
! [X] : plus(X,n1) = succ(X),
file('theBenchmark.p',succ_plus_1_r) ).
fof(succ_plus_1_l,axiom,
! [X] : plus(n1,X) = succ(X),
file('theBenchmark.p',succ_plus_1_l) ).
fof(pred_minus_1,axiom,
! [X] : minus(X,n1) = pred(X),
file('theBenchmark.p',pred_minus_1) ).
fof(succ_pred,axiom,
! [X] : succ(pred(X)) = X,
file('theBenchmark.p',succ_pred) ).
fof(finite_domain_0,axiom,
! [X] :
( ( leq(X,n0)
& leq(n0,X) )
=> X = n0 ),
file('theBenchmark.p',finite_domain_0) ).
fof(gauss_init_0077,conjecture,
( ( geq(minus(n410,n1),n0)
& geq(minus(n330,n1),n0) )
=> ! [A] :
( ( leq(A,n2)
& leq(n0,A) )
=> ! [B] :
( ( leq(B,minus(n0,n1))
& leq(n0,B) )
=> a_select3(tptp_const_array2(dim(n0,n3),dim(n0,n2),uninit),B,A) = init ) ) ),
file('theBenchmark.p',gauss_init_0077) ).
fof(gauss_init_0077_neg,negated_conjecture,
~ ( ( geq(minus(n410,n1),n0)
& geq(minus(n330,n1),n0) )
=> ! [A] :
( ( leq(A,n2)
& leq(n0,A) )
=> ! [B] :
( ( leq(B,minus(n0,n1))
& leq(n0,B) )
=> a_select3(tptp_const_array2(dim(n0,n3),dim(n0,n2),uninit),B,A) = init ) ) ),
inference(assume_negation,[status(cth)],[gauss_init_0077]) ).
cnf(c_67,plain,
~ gt(A,A),
inference(clausify,[status(thm)],[irreflexivity_gt]) ).
cnf(c_75,plain,
( leq(A,succ(B))
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_succ]) ).
cnf(c_76,plain,
( gt(succ(B),A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_succ_gt_equiv]) ).
cnf(c_286,plain,
plus(A,n1) = succ(A),
inference(clausify,[status(thm)],[succ_plus_1_r]) ).
cnf(c_287,plain,
succ(A) = plus(A,n1),
inference(copy,[status(thm)],[c_286]) ).
cnf(c_288,plain,
plus(n1,A) = succ(A),
inference(clausify,[status(thm)],[succ_plus_1_l]) ).
cnf(c_289,plain,
plus(n1,A) = plus(A,n1),
inference(paramod,[status(thm)],[c_287,c_288]) ).
cnf(c_306,plain,
minus(A,n1) = pred(A),
inference(clausify,[status(thm)],[pred_minus_1]) ).
cnf(c_307,plain,
pred(A) = minus(A,n1),
inference(copy,[status(thm)],[c_306]) ).
cnf(c_310,plain,
succ(pred(A)) = A,
inference(clausify,[status(thm)],[succ_pred]) ).
cnf(c_1564,plain,
succ(minus(A,n1)) = A,
inference(paramod,[status(thm)],[c_307,c_310]) ).
cnf(c_1565,plain,
plus(minus(A,n1),n1) = A,
inference(paramod,[status(thm)],[c_287,c_1564]) ).
cnf(c_311,plain,
plus(n1,minus(A,n1)) = A,
inference(paramod,[status(thm)],[c_289,c_1565]) ).
cnf(c_372,plain,
( n0 = A
| ~ leq(A,n0)
| ~ leq(n0,A) ),
inference(clausify,[status(thm)],[finite_domain_0]) ).
fof(nnf_56,plain,
( ? [A] :
( ? [B] :
( a_select3(tptp_const_array2(dim(n0,n3),dim(n0,n2),uninit),B,A) != init
& leq(B,minus(n0,n1))
& leq(n0,B) )
& leq(A,n2)
& leq(n0,A) )
& geq(minus(n410,n1),n0)
& geq(minus(n330,n1),n0) ),
inference(fof_nnf,[status(thm)],[gauss_init_0077_neg]) ).
fof(sk_gauss_init_0077_neg,plain,
( a_select3(tptp_const_array2(dim(n0,n3),dim(n0,n2),uninit),sK0,sK1) != init
& leq(sK0,minus(n0,n1))
& leq(n0,sK0)
& leq(sK1,n2)
& leq(n0,sK1)
& geq(minus(n410,n1),n0)
& geq(minus(n330,n1),n0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_56]) ).
cnf(c_388,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_gauss_init_0077_neg]) ).
cnf(c_389,negated_conjecture,
leq(sK0,minus(n0,n1)),
inference(split_conjunct,[status(thm)],[sk_gauss_init_0077_neg]) ).
cnf(c_825,plain,
( gt(plus(B,n1),A)
| ~ leq(A,B) ),
inference(paramod,[status(thm)],[c_287,c_76]) ).
cnf(c_826,plain,
( leq(A,plus(B,n1))
| ~ leq(A,B) ),
inference(paramod,[status(thm)],[c_287,c_75]) ).
cnf(c_1566,negated_conjecture,
( n0 = sK0
| ~ leq(sK0,n0) ),
inference(resolve,[status(thm)],[c_388,c_372]) ).
cnf(c_1351,negated_conjecture,
( sK0 = n0
| ~ leq(sK0,n0) ),
inference(copy,[status(thm)],[c_1566]) ).
cnf(c_1567,negated_conjecture,
gt(plus(minus(n0,n1),n1),sK0),
inference(resolve,[status(thm)],[c_825,c_389]) ).
cnf(c_1568,negated_conjecture,
gt(plus(n1,minus(n0,n1)),sK0),
inference(paramod,[status(thm)],[c_289,c_1567]) ).
cnf(c_1543,negated_conjecture,
gt(n0,sK0),
inference(paramod,[status(thm)],[c_311,c_1568]) ).
cnf(c_1569,negated_conjecture,
leq(sK0,plus(minus(n0,n1),n1)),
inference(resolve,[status(thm)],[c_826,c_389]) ).
cnf(c_1570,negated_conjecture,
leq(sK0,plus(n1,minus(n0,n1))),
inference(paramod,[status(thm)],[c_289,c_1569]) ).
cnf(c_1547,negated_conjecture,
leq(sK0,n0),
inference(paramod,[status(thm)],[c_311,c_1570]) ).
cnf(c_1562,negated_conjecture,
sK0 = n0,
inference(resolve,[status(thm)],[c_1547,c_1351]) ).
cnf(c_1571,negated_conjecture,
gt(n0,n0),
inference(paramod,[status(thm)],[c_1562,c_1543]) ).
cnf(c_1563,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_67,c_1571]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV041+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sat Sep 26 13:07:34 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.30 % Process 678949 was started by sandbox2 on n012,
% 0.02/0.30 % Sat Sep 26 13:07:34 2026
% 0.02/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 10.65/1.78
% 10.65/1.78 % given #500 (I,wt=116): 593 leq(n0,f19(A,B,C,D,E,F,n0,V6)) | leq(n0,f22(A,B,C,D,E,F,n0,V6)) | leq(n0,f23(A,B,C,D,E,F,n0,V6)) | -leq(n0,V7) | -leq(V7,n0) | a_select3(tptp_madd(A,tptp_mmul(B,tptp_mmul(tptp_madd(tptp_mmul(C,tptp_mmul(D,trans(C))),tptp_mmul(E,tptp_mmul(F,trans(E)))),trans(B)))),n0,V7) = a_select3(tptp_madd(A,tptp_mmul(B,tptp_mmul(tptp_madd(tptp_mmul(C,tptp_mmul(D,trans(C))),tptp_mmul(E,tptp_mmul(F,trans(E)))),trans(B)))),V7,n0). [factor(167,d,e),flip(g),unit_del(d,68)].
% 10.65/1.78
% 10.65/1.78 % SZS status Theorem for theBenchmark
% 10.65/1.78
% 10.65/1.78 % Proof 1 at 1.20 (+ 0.19) seconds.
% 10.65/1.78 % Length of proof is 30.
% 10.65/1.78 % Level of proof is 7.
% 10.65/1.78 % Maximum clause weight is 13.000.
% 10.65/1.78 % Given clauses 733.
% 10.65/1.78
% 10.65/1.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------