%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV136+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 09:06:52 AM UTC 2026
% Result : Theorem 14.43s 2.52s
% Output : CNFRefutation 14.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 22 unt; 0 def)
% Number of atoms : 64 ( 14 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 40 ( 10 ~; 8 |; 17 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity_gt,axiom,
! [X,Y,Z] :
( ( gt(Y,Z)
& gt(X,Y) )
=> gt(X,Z) ),
file('theBenchmark.p',transitivity_gt) ).
fof(leq_gt1,axiom,
! [X,Y] :
( gt(Y,X)
=> leq(X,Y) ),
file('theBenchmark.p',leq_gt1) ).
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(leq_succ_gt,axiom,
! [X,Y] :
( leq(succ(X),Y)
=> gt(Y,X) ),
file('theBenchmark.p',leq_succ_gt) ).
fof(gauss_array_0006,conjecture,
( ( leq(a_select2(s_values7,pv1325),a_select2(s_values7,s_best7))
& leq(pv1325,n3)
& leq(s_worst7,n3)
& leq(s_sworst7,n3)
& leq(s_best7,n3)
& leq(n2,pv1325)
& leq(n0,s_worst7)
& leq(n0,s_sworst7)
& leq(n0,s_best7) )
=> leq(n0,pv1325) ),
file('theBenchmark.p',gauss_array_0006) ).
fof(gauss_array_0006_neg,negated_conjecture,
~ ( ( leq(a_select2(s_values7,pv1325),a_select2(s_values7,s_best7))
& leq(pv1325,n3)
& leq(s_worst7,n3)
& leq(s_sworst7,n3)
& leq(s_best7,n3)
& leq(n2,pv1325)
& leq(n0,s_worst7)
& leq(n0,s_sworst7)
& leq(n0,s_best7) )
=> leq(n0,pv1325) ),
inference(assume_negation,[status(cth)],[gauss_array_0006]) ).
cnf(c_62,plain,
( gt(A,C)
| ~ gt(B,C)
| ~ gt(A,B) ),
inference(clausify,[status(thm)],[transitivity_gt]) ).
cnf(c_66,plain,
( leq(B,A)
| ~ gt(A,B) ),
inference(clausify,[status(thm)],[leq_gt1]) ).
cnf(c_282,plain,
plus(A,n1) = succ(A),
inference(clausify,[status(thm)],[succ_plus_1_r]) ).
cnf(c_283,plain,
succ(A) = plus(A,n1),
inference(copy,[status(thm)],[c_282]) ).
cnf(c_284,plain,
plus(n1,A) = succ(A),
inference(clausify,[status(thm)],[succ_plus_1_l]) ).
cnf(c_285,plain,
plus(n1,A) = plus(A,n1),
inference(paramod,[status(thm)],[c_283,c_284]) ).
cnf(c_312,plain,
( gt(B,A)
| ~ leq(succ(A),B) ),
inference(clausify,[status(thm)],[leq_succ_gt]) ).
cnf(c_313,plain,
( gt(B,A)
| ~ leq(plus(A,n1),B) ),
inference(paramod,[status(thm)],[c_283,c_312]) ).
fof(gt_1_0,axiom,
gt(n1,n0),
file('theBenchmark.p',gt_1_0) ).
cnf(c_339,plain,
gt(n1,n0),
inference(clausify,[status(thm)],[gt_1_0]) ).
fof(successor_1,axiom,
succ(n0) = n1,
file('theBenchmark.p',successor_1) ).
cnf(c_361,plain,
succ(n0) = n1,
inference(clausify,[status(thm)],[successor_1]) ).
cnf(c_362,plain,
plus(n0,n1) = n1,
inference(paramod,[status(thm)],[c_283,c_361]) ).
fof(successor_2,axiom,
succ(succ(n0)) = n2,
file('theBenchmark.p',successor_2) ).
cnf(c_363,plain,
succ(succ(n0)) = n2,
inference(clausify,[status(thm)],[successor_2]) ).
cnf(c_12619,plain,
succ(plus(n0,n1)) = n2,
inference(paramod,[status(thm)],[c_283,c_363]) ).
cnf(c_12620,plain,
succ(n1) = n2,
inference(paramod,[status(thm)],[c_362,c_12619]) ).
cnf(c_364,plain,
plus(n1,n1) = n2,
inference(paramod,[status(thm)],[c_283,c_12620]) ).
cnf(c_370,negated_conjecture,
leq(n2,pv1325),
inference(clausify,[status(thm)],[gauss_array_0006_neg]) ).
cnf(c_376,negated_conjecture,
~ leq(n0,pv1325),
inference(clausify,[status(thm)],[gauss_array_0006_neg]) ).
cnf(c_12621,plain,
( gt(A,n1)
| ~ leq(plus(n1,n1),A) ),
inference(paramod,[status(thm)],[c_285,c_313]) ).
cnf(c_1192,plain,
( gt(A,n1)
| ~ leq(n2,A) ),
inference(paramod,[status(thm)],[c_364,c_12621]) ).
cnf(c_1289,plain,
( gt(A,n0)
| ~ gt(A,n1) ),
inference(resolve,[status(thm)],[c_339,c_62]) ).
cnf(c_11921,plain,
gt(pv1325,n1),
inference(resolve,[status(thm)],[c_1192,c_370]) ).
cnf(c_12613,plain,
gt(pv1325,n0),
inference(resolve,[status(thm)],[c_1289,c_11921]) ).
cnf(c_12622,plain,
leq(n0,pv1325),
inference(resolve,[status(thm)],[c_12613,c_66]) ).
cnf(c_12618,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_376,c_12622]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV136+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n020.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 13:15:50 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 1664097 was started by sandbox on n020,
% 0.09/0.38 % Sat Sep 26 13:15:50 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.43
% 0.09/0.43 % From the command line: assign(max_seconds, 300).
% 14.43/2.52
% 14.43/2.52 % given #500 (I,wt=158): 590 leq(n0,f19(A,B,C,D,E,F,V6,V7)) | leq(f22(A,B,C,D,E,F,V6,V7),V6) | leq(n0,f23(A,B,C,D,E,F,V6,V7)) | -leq(n0,V6) | 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,V6) = 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)))),V6,n0). [factor(168,d,g),unit_del(e,64),unit_del(f,64)].
% 14.43/2.52
% 14.43/2.52 % SZS status Theorem for theBenchmark
% 14.43/2.52
% 14.43/2.52 % Proof 1 at 1.70 (+ 0.35) seconds.
% 14.43/2.52 % Length of proof is 26.
% 14.43/2.52 % Level of proof is 8.
% 14.43/2.52 % Maximum clause weight is 18.000.
% 14.43/2.52 % Given clauses 883.
% 14.43/2.52
% 14.43/2.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------