%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV199+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 : Fri Sep 25 03:12:28 PM UTC 2026
% Result : Theorem 85.48s 12.03s
% Output : Proof 85.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 75
% Number of leaves : 20
% Syntax : Number of formulae : 223 ( 192 unt; 0 def)
% Number of atoms : 470 ( 339 equ)
% Maximal formula atoms : 51 ( 2 avg)
% Number of connectives : 330 ( 83 ~; 56 |; 175 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 46 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 21 con; 0-4 aty)
% Number of variables : 131 ( 2 sgn 62 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
! [X,Y] :
( leq(succ(X),Y)
=> gt(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt) ).
fof(f42_nnf,plain,
! [X,Y] :
( gt(Y,X)
| ~ leq(succ(X),Y) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [X,Y] :
( gt(Y,X)
| ~ leq(succ(X),Y) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c239,plain,
( gt(X1,X0)
| ~ leq(succ(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(t185,plain,
ifeq(leq(succ(X1),X2),trueq,gt(X2,X1),trueq) = trueq,
inference(equality_encoding,[status(esa)],[c239]) ).
cnf(t1035,plain,
ifeq(leq(succ(X1),X2),trueq,gt(X2,X1),trueq) = trueq,
inference(orient,[status(thm)],[t185]) ).
fof(f2,axiom,
! [X] : ~ gt(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_gt) ).
fof(f2_nnf,plain,
! [X] : ~ gt(X,X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : ~ gt(X,X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ gt(X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t43,plain,
gt(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t1461,plain,
gt(X1,X1) = false,
inference(orient,[status(thm)],[t43]) ).
cnf(t1467,plain,
trueq = ifeq(leq(succ(X1),X1),trueq,false,trueq),
inference(cp,[status(thm)],[t1035,t1461]) ).
cnf(t4409,plain,
ifeq(leq(succ(X1),X1),trueq,false,trueq) = trueq,
inference(orient,[status(thm)],[t1467]) ).
fof(f91,axiom,
succ(succ(succ(n0))) = n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_3) ).
fof(f91_nnf,plain,
succ(succ(succ(n0))) = n3,
inference(nnf_transformation,[status(thm)],[f91]) ).
cnf(c333,plain,
succ(succ(succ(n0))) = n3,
inference(cnf_transformation,[status(esa)],[f91_nnf]) ).
cnf(t113,plain,
succ(succ(succ(n0))) = n3,
inference(equality_encoding,[status(esa)],[c333]) ).
fof(f83,axiom,
! [X] :
( ( leq(X,n0)
& leq(n0,X) )
=> X = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_0) ).
fof(f83_nnf,plain,
! [X] :
( X = n0
| ~ leq(X,n0)
| ~ leq(n0,X) ),
inference(nnf_transformation,[status(thm)],[f83]) ).
fof(f83_sk,plain,
! [X] :
( X = n0
| ~ leq(X,n0)
| ~ leq(n0,X) ),
inference(skolemisation,[status(esa)],[f83_nnf]) ).
cnf(c325,plain,
( X0 = n0
| ~ leq(X0,n0)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(esa)],[f83_sk]) ).
cnf(hi319,axiom,
ifeq(leq(n0,X0),trueq,ifeq(leq(X0,n0),trueq,X0,n0),n0) = n0,
inference(equality_encoding,[status(esa)],[c325]) ).
fof(f52,conjecture,
( ( ! [C,D] :
( ( leq(D,pred(pv5))
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(z_defuse,C,D) = use )
& ! [A,B] :
( ( leq(B,pred(pv5))
& leq(A,n2)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(u_defuse,A,B) = use )
& leq(pv5,n998)
& leq(pv5,n0)
& leq(n0,pv5)
& a_select2(xinit_noise_defuse,n5) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n3) = use
& a_select3(u_defuse,n2,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n0,n0) = use
& a_select2(sigma_defuse,n5) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(rho_defuse,n2) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n0) = use )
=> ! [E,F] :
( ( leq(F,pv5)
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
=> ( ( ~ ( pv5 = F
& n2 = E )
& ~ ( pv5 = F
& n1 = E )
& ~ ( pv5 = F
& n0 = E ) )
=> a_select3(z_defuse,E,F) = use ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_inuse_0010) ).
fof(f52_neg,negated_conjecture,
~ ( ( ! [C,D] :
( ( leq(D,pred(pv5))
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(z_defuse,C,D) = use )
& ! [A,B] :
( ( leq(B,pred(pv5))
& leq(A,n2)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(u_defuse,A,B) = use )
& leq(pv5,n998)
& leq(pv5,n0)
& leq(n0,pv5)
& a_select2(xinit_noise_defuse,n5) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n3) = use
& a_select3(u_defuse,n2,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n0,n0) = use
& a_select2(sigma_defuse,n5) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(rho_defuse,n2) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n0) = use )
=> ! [E,F] :
( ( leq(F,pv5)
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
=> ( ( ~ ( pv5 = F
& n2 = E )
& ~ ( pv5 = F
& n1 = E )
& ~ ( pv5 = F
& n0 = E ) )
=> a_select3(z_defuse,E,F) = use ) ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
( ? [E,F] :
( a_select3(z_defuse,E,F) != use
& ( pv5 != F
| n2 != E )
& ( pv5 != F
| n1 != E )
& ( pv5 != F
| n0 != E )
& leq(F,pv5)
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
& ! [C,D] :
( a_select3(z_defuse,C,D) = use
| ~ leq(D,pred(pv5))
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(u_defuse,A,B) = use
| ~ leq(B,pred(pv5))
| ~ leq(A,n2)
| ~ leq(n0,B)
| ~ leq(n0,A) )
& leq(pv5,n998)
& leq(pv5,n0)
& leq(n0,pv5)
& a_select2(xinit_noise_defuse,n5) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n3) = use
& a_select3(u_defuse,n2,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n0,n0) = use
& a_select2(sigma_defuse,n5) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(rho_defuse,n2) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n0) = use ),
inference(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
! [A,B,C,D] :
( a_select3(z_defuse,sk27,sk28) != use
& ( pv5 != sk28
| n2 != sk27 )
& ( pv5 != sk28
| n1 != sk27 )
& ( pv5 != sk28
| n0 != sk27 )
& leq(sk28,pv5)
& leq(sk27,n2)
& leq(n0,sk28)
& leq(n0,sk27)
& ( a_select3(z_defuse,C,D) = use
| ~ leq(D,pred(pv5))
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ( a_select3(u_defuse,A,B) = use
| ~ leq(B,pred(pv5))
| ~ leq(A,n2)
| ~ leq(n0,B)
| ~ leq(n0,A) )
& leq(pv5,n998)
& leq(pv5,n0)
& leq(n0,pv5)
& a_select2(xinit_noise_defuse,n5) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n3) = use
& a_select3(u_defuse,n2,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n0,n0) = use
& a_select2(sigma_defuse,n5) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(rho_defuse,n2) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n0) = use ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk27,sk28])],[f52_nnf]) ).
cnf(c282,plain,
leq(n0,pv5),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi280,negated_conjecture,
leq(n0,pv5) = trueq,
inference(equality_encoding,[status(esa)],[c282]) ).
cnf(c283,plain,
leq(pv5,n0),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi281,negated_conjecture,
leq(pv5,n0) = trueq,
inference(equality_encoding,[status(esa)],[c283]) ).
cnf(t0,plain,
pv5 = n0,
inference(hyper_resolution,[status(thm)],[hi319,hi280,hi281]) ).
cnf(t1356,plain,
n0 = pv5,
inference(orient,[status(thm)],[t0]) ).
fof(f4,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& leq(X,Y) )
=> leq(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_leq) ).
fof(f4_nnf,plain,
! [X,Y,Z] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
ifeq(leq(X0,X1),trueq,ifeq(leq(X1,X2),trueq,leq(X0,X2),trueq),trueq) = trueq,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(c290,plain,
leq(sk28,pv5),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi288,negated_conjecture,
leq(sk28,pv5) = trueq,
inference(equality_encoding,[status(esa)],[c290]) ).
cnf(h4871,plain,
leq(sk28,n0) = trueq,
inference(hyper_resolution,[status(thm)],[hi3,hi288,hi281]) ).
cnf(c288,plain,
leq(n0,sk28),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi286,negated_conjecture,
leq(n0,sk28) = trueq,
inference(equality_encoding,[status(esa)],[c288]) ).
cnf(t1,plain,
sk28 = n0,
inference(hyper_resolution,[status(thm)],[hi319,hi286,h4871]) ).
cnf(t22960,plain,
sk28 = pv5,
inference(step,[status(thm)],[t1,t1356]) ).
cnf(t1418,plain,
pv5 = sk28,
inference(orient,[status(thm)],[t22960]) ).
cnf(t22961,plain,
n0 = sk28,
inference(step,[status(thm)],[t1356,t1418]) ).
cnf(t1419,plain,
n0 = sk28,
inference(orient,[status(thm)],[t22961]) ).
cnf(t23006,plain,
succ(succ(succ(sk28))) = n3,
inference(step,[status(thm)],[t113,t1419]) ).
fof(f89,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
fof(f89_nnf,plain,
succ(n0) = n1,
inference(nnf_transformation,[status(thm)],[f89]) ).
cnf(c331,plain,
succ(n0) = n1,
inference(cnf_transformation,[status(esa)],[f89_nnf]) ).
cnf(t4,plain,
succ(n0) = n1,
inference(equality_encoding,[status(esa)],[c331]) ).
cnf(t22988,plain,
succ(sk28) = n1,
inference(step,[status(thm)],[t4,t1419]) ).
cnf(t1453,plain,
succ(sk28) = n1,
inference(orient,[status(thm)],[t22988]) ).
cnf(t23007,plain,
succ(succ(n1)) = n3,
inference(step,[status(thm)],[t23006,t1453]) ).
cnf(t1542,plain,
succ(succ(n1)) = n3,
inference(orient,[status(thm)],[t23007]) ).
fof(f90,axiom,
succ(succ(n0)) = n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_2) ).
fof(f90_nnf,plain,
succ(succ(n0)) = n2,
inference(nnf_transformation,[status(thm)],[f90]) ).
cnf(c332,plain,
succ(succ(n0)) = n2,
inference(cnf_transformation,[status(esa)],[f90_nnf]) ).
cnf(t109,plain,
succ(succ(n0)) = n2,
inference(equality_encoding,[status(esa)],[c332]) ).
cnf(t22983,plain,
succ(succ(sk28)) = n2,
inference(step,[status(thm)],[t109,t1419]) ).
cnf(t1437,plain,
succ(succ(sk28)) = n2,
inference(orient,[status(thm)],[t22983]) ).
cnf(t22989,plain,
succ(n1) = n2,
inference(step,[status(thm)],[t1437,t1453]) ).
cnf(t1460,plain,
succ(n1) = n2,
inference(rw,[status(thm)],[t22989]) ).
cnf(t1553,plain,
succ(n1) = n2,
inference(orient,[status(thm)],[t1460]) ).
cnf(t23009,plain,
succ(n2) = n3,
inference(step,[status(thm)],[t1542,t1553]) ).
cnf(t1560,plain,
succ(n2) = n3,
inference(rw,[status(thm)],[t23009]) ).
cnf(t1574,plain,
succ(n2) = n3,
inference(orient,[status(thm)],[t1560]) ).
cnf(t4410,plain,
trueq = ifeq(leq(n3,n2),trueq,false,trueq),
inference(cp,[status(thm)],[t4409,t1574]) ).
cnf(t4416,plain,
ifeq(leq(n3,n2),trueq,false,trueq) = trueq,
inference(orient,[status(thm)],[t4410]) ).
cnf(t219,plain,
ifeq(leq(X1,X2),trueq,ifeq(leq(X2,X3),trueq,leq(X1,X3),trueq),trueq) = trueq,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t841,plain,
ifeq(leq(X1,X2),trueq,ifeq(leq(X2,X3),trueq,leq(X1,X3),trueq),trueq) = trueq,
inference(orient,[status(thm)],[t219]) ).
cnf(c289,plain,
leq(sk27,n2),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(t97,plain,
leq(sk27,n2) = trueq,
inference(equality_encoding,[status(esa)],[c289]) ).
cnf(t678,plain,
leq(sk27,n2) = trueq,
inference(orient,[status(thm)],[t97]) ).
cnf(t879,plain,
trueq = ifeq(leq(X1,sk27),trueq,ifeq(trueq,trueq,leq(X1,n2),trueq),trueq),
inference(cp,[status(thm)],[t841,t678]) ).
cnf(t137,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t306,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t137]) ).
cnf(t23798,plain,
trueq = ifeq(leq(X1,sk27),trueq,leq(X1,n2),trueq),
inference(step,[status(thm)],[t879,t306]) ).
cnf(t14053,plain,
ifeq(leq(X1,sk27),trueq,leq(X1,n2),trueq) = trueq,
inference(orient,[status(thm)],[t23798]) ).
fof(f41,axiom,
! [X,Y] :
( leq(succ(X),succ(Y))
<=> leq(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_succ) ).
fof(f41_nnf,plain,
! [X,Y] :
( ( ~ leq(X,Y)
| leq(succ(X),succ(Y)) )
& ( leq(X,Y)
| ~ leq(succ(X),succ(Y)) ) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [X,Y] :
( ( ~ leq(X,Y)
| leq(succ(X),succ(Y)) )
& ( leq(X,Y)
| ~ leq(succ(X),succ(Y)) ) ),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c238,plain,
( ~ leq(X0,X1)
| leq(succ(X0),succ(X1)) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(t215,plain,
ifeq(leq(X1,X2),trueq,leq(succ(X1),succ(X2)),trueq) = trueq,
inference(equality_encoding,[status(esa)],[c238]) ).
cnf(t803,plain,
ifeq(leq(X1,X2),trueq,leq(succ(X1),succ(X2)),trueq) = trueq,
inference(orient,[status(thm)],[t215]) ).
fof(f9,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt_pred) ).
fof(f9_nnf,plain,
! [X,Y] :
( ( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ( gt(Y,X)
| ~ leq(X,pred(Y)) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y] :
( ( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ( gt(Y,X)
| ~ leq(X,pred(Y)) ) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c12,plain,
( ~ gt(X1,X0)
| leq(X0,pred(X1)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t183,plain,
ifeq(gt(X1,X2),trueq,leq(X2,pred(X1)),trueq) = trueq,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t1160,plain,
ifeq(gt(X1,X2),trueq,leq(X2,pred(X1)),trueq) = trueq,
inference(orient,[status(thm)],[t183]) ).
cnf(t173,plain,
ifeq(eq(X1,X2),trueq,X1,X2) = X2,
introduced(definition) ).
cnf(t307,plain,
ifeq(eq(X1,X2),trueq,X1,X2) = X2,
inference(orient,[status(thm)],[t173]) ).
fof(f8,axiom,
! [X,Y] :
( ( X != Y
& leq(X,Y) )
=> gt(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt2) ).
fof(f8_nnf,plain,
! [X,Y] :
( gt(Y,X)
| X = Y
| ~ leq(X,Y) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( gt(Y,X)
| X = Y
| ~ leq(X,Y) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c10,plain,
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t220,plain,
ifeq(leq(X1,X2),trueq,or(eq(X1,X2),eq(gt(X2,X1),trueq)),trueq) = trueq,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t765,plain,
ifeq(leq(X1,X2),trueq,or(eq(X1,X2),eq(gt(X2,X1),trueq)),trueq) = trueq,
inference(orient,[status(thm)],[t220]) ).
cnf(t140,plain,
ifeq(not(X1),trueq,X1,false) = false,
introduced(definition) ).
cnf(t1539,plain,
ifeq(not(X1),trueq,X1,false) = false,
inference(orient,[status(thm)],[t140]) ).
cnf(c291,plain,
( pv5 != sk28
| n0 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(t180,plain,
or(not(eq(n0,sk27)),not(eq(pv5,sk28))) = trueq,
inference(equality_encoding,[status(esa)],[c291]) ).
cnf(t430,plain,
or(not(eq(n0,sk27)),not(eq(pv5,sk28))) = trueq,
inference(orient,[status(thm)],[t180]) ).
cnf(t22886,plain,
or(not(eq(pv5,sk27)),not(eq(pv5,sk28))) = trueq,
inference(step,[status(thm)],[t430,t1356]) ).
cnf(t1372,plain,
or(not(eq(pv5,sk27)),not(eq(pv5,sk28))) = trueq,
inference(rw,[status(thm)],[t22886]) ).
cnf(t24171,plain,
or(not(eq(sk28,sk27)),not(eq(pv5,sk28))) = trueq,
inference(step,[status(thm)],[t1372,t1418]) ).
cnf(t24172,plain,
or(not(eq(sk28,sk27)),not(eq(sk28,sk28))) = trueq,
inference(step,[status(thm)],[t24171,t1418]) ).
cnf(t29,plain,
eq(X1,X1) = trueq,
introduced(definition) ).
cnf(t360,plain,
eq(X1,X1) = trueq,
inference(orient,[status(thm)],[t29]) ).
cnf(t24173,plain,
or(not(eq(sk28,sk27)),not(trueq)) = trueq,
inference(step,[status(thm)],[t24172,t360]) ).
cnf(t3,plain,
not(trueq) = false,
introduced(definition) ).
cnf(t1540,plain,
not(trueq) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t24174,plain,
or(not(eq(sk28,sk27)),false) = trueq,
inference(step,[status(thm)],[t24173,t1540]) ).
cnf(t103,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t276,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t103]) ).
cnf(t24175,plain,
not(eq(sk28,sk27)) = trueq,
inference(step,[status(thm)],[t24174,t276]) ).
cnf(t22363,plain,
not(eq(sk28,sk27)) = trueq,
inference(orient,[status(thm)],[t24175]) ).
cnf(t22364,plain,
false = ifeq(trueq,trueq,eq(sk28,sk27),false),
inference(cp,[status(thm)],[t1539,t22363]) ).
cnf(t24176,plain,
false = eq(sk28,sk27),
inference(step,[status(thm)],[t22364,t306]) ).
cnf(t22365,plain,
eq(sk28,sk27) = false,
inference(orient,[status(thm)],[t24176]) ).
cnf(t22367,plain,
trueq = ifeq(leq(sk28,sk27),trueq,or(false,eq(gt(sk27,sk28),trueq)),trueq),
inference(cp,[status(thm)],[t765,t22365]) ).
cnf(c287,plain,
leq(n0,sk27),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi285,negated_conjecture,
leq(n0,sk27) = trueq,
inference(equality_encoding,[status(esa)],[c287]) ).
cnf(h2855,plain,
leq(pv5,sk27) = trueq,
inference(hyper_resolution,[status(thm)],[hi3,hi281,hi285]) ).
cnf(t102,plain,
leq(sk28,sk27) = trueq,
inference(hyper_resolution,[status(thm)],[hi3,hi288,h2855]) ).
cnf(t650,plain,
leq(sk28,sk27) = trueq,
inference(orient,[status(thm)],[t102]) ).
cnf(t24179,plain,
trueq = ifeq(trueq,trueq,or(false,eq(gt(sk27,sk28),trueq)),trueq),
inference(step,[status(thm)],[t22367,t650]) ).
cnf(t24180,plain,
trueq = or(false,eq(gt(sk27,sk28),trueq)),
inference(step,[status(thm)],[t24179,t306]) ).
cnf(t105,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t277,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t105]) ).
cnf(t24181,plain,
trueq = eq(gt(sk27,sk28),trueq),
inference(step,[status(thm)],[t24180,t277]) ).
cnf(t22376,plain,
eq(gt(sk27,sk28),trueq) = trueq,
inference(orient,[status(thm)],[t24181]) ).
cnf(t22377,plain,
trueq = ifeq(trueq,trueq,gt(sk27,sk28),trueq),
inference(cp,[status(thm)],[t307,t22376]) ).
cnf(t24182,plain,
trueq = gt(sk27,sk28),
inference(step,[status(thm)],[t22377,t306]) ).
cnf(t22380,plain,
gt(sk27,sk28) = trueq,
inference(orient,[status(thm)],[t24182]) ).
cnf(t22384,plain,
trueq = ifeq(trueq,trueq,leq(sk28,pred(sk27)),trueq),
inference(cp,[status(thm)],[t1160,t22380]) ).
cnf(t24183,plain,
trueq = leq(sk28,pred(sk27)),
inference(step,[status(thm)],[t22384,t306]) ).
cnf(t22386,plain,
leq(sk28,pred(sk27)) = trueq,
inference(orient,[status(thm)],[t24183]) ).
cnf(t22394,plain,
trueq = ifeq(trueq,trueq,leq(succ(sk28),succ(pred(sk27))),trueq),
inference(cp,[status(thm)],[t803,t22386]) ).
cnf(t24184,plain,
trueq = leq(succ(sk28),succ(pred(sk27))),
inference(step,[status(thm)],[t22394,t306]) ).
cnf(t24185,plain,
trueq = leq(n1,succ(pred(sk27))),
inference(step,[status(thm)],[t24184,t1453]) ).
fof(f40,axiom,
! [X] : succ(pred(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_pred) ).
fof(f40_nnf,plain,
! [X] : succ(pred(X)) = X,
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [X] : succ(pred(X)) = X,
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c236,plain,
succ(pred(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(t108,plain,
succ(pred(X1)) = X1,
inference(equality_encoding,[status(esa)],[c236]) ).
cnf(t358,plain,
succ(pred(X1)) = X1,
inference(orient,[status(thm)],[t108]) ).
cnf(t24186,plain,
trueq = leq(n1,sk27),
inference(step,[status(thm)],[t24185,t358]) ).
cnf(t22428,plain,
leq(n1,sk27) = trueq,
inference(orient,[status(thm)],[t24186]) ).
cnf(t22437,plain,
trueq = ifeq(trueq,trueq,or(eq(n1,sk27),eq(gt(sk27,n1),trueq)),trueq),
inference(cp,[status(thm)],[t765,t22428]) ).
cnf(t24190,plain,
trueq = or(eq(n1,sk27),eq(gt(sk27,n1),trueq)),
inference(step,[status(thm)],[t22437,t306]) ).
cnf(c292,plain,
( pv5 != sk28
| n1 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(t181,plain,
or(not(eq(n1,sk27)),not(eq(pv5,sk28))) = trueq,
inference(equality_encoding,[status(esa)],[c292]) ).
cnf(t432,plain,
or(not(eq(n1,sk27)),not(eq(pv5,sk28))) = trueq,
inference(orient,[status(thm)],[t181]) ).
cnf(t22979,plain,
or(not(eq(n1,sk27)),not(eq(sk28,sk28))) = trueq,
inference(step,[status(thm)],[t432,t1418]) ).
cnf(t22980,plain,
or(not(eq(n1,sk27)),not(trueq)) = trueq,
inference(step,[status(thm)],[t22979,t360]) ).
cnf(t1429,plain,
or(not(eq(n1,sk27)),not(trueq)) = trueq,
inference(rw,[status(thm)],[t22980]) ).
cnf(t23252,plain,
or(not(eq(n1,sk27)),false) = trueq,
inference(step,[status(thm)],[t1429,t1540]) ).
cnf(t23253,plain,
not(eq(n1,sk27)) = trueq,
inference(step,[status(thm)],[t23252,t276]) ).
cnf(t3692,plain,
not(eq(n1,sk27)) = trueq,
inference(orient,[status(thm)],[t23253]) ).
cnf(t3693,plain,
false = ifeq(trueq,trueq,eq(n1,sk27),false),
inference(cp,[status(thm)],[t1539,t3692]) ).
cnf(t23254,plain,
false = eq(n1,sk27),
inference(step,[status(thm)],[t3693,t306]) ).
cnf(t3694,plain,
eq(n1,sk27) = false,
inference(orient,[status(thm)],[t23254]) ).
cnf(t24191,plain,
trueq = or(false,eq(gt(sk27,n1),trueq)),
inference(step,[status(thm)],[t24190,t3694]) ).
cnf(t24192,plain,
trueq = eq(gt(sk27,n1),trueq),
inference(step,[status(thm)],[t24191,t277]) ).
cnf(t22521,plain,
eq(gt(sk27,n1),trueq) = trueq,
inference(orient,[status(thm)],[t24192]) ).
cnf(t22522,plain,
trueq = ifeq(trueq,trueq,gt(sk27,n1),trueq),
inference(cp,[status(thm)],[t307,t22521]) ).
cnf(t24193,plain,
trueq = gt(sk27,n1),
inference(step,[status(thm)],[t22522,t306]) ).
cnf(t22525,plain,
gt(sk27,n1) = trueq,
inference(orient,[status(thm)],[t24193]) ).
cnf(t22534,plain,
trueq = ifeq(trueq,trueq,leq(n1,pred(sk27)),trueq),
inference(cp,[status(thm)],[t1160,t22525]) ).
cnf(t24194,plain,
trueq = leq(n1,pred(sk27)),
inference(step,[status(thm)],[t22534,t306]) ).
cnf(t22536,plain,
leq(n1,pred(sk27)) = trueq,
inference(orient,[status(thm)],[t24194]) ).
cnf(t22546,plain,
trueq = ifeq(trueq,trueq,leq(succ(n1),succ(pred(sk27))),trueq),
inference(cp,[status(thm)],[t803,t22536]) ).
cnf(t24195,plain,
trueq = leq(succ(n1),succ(pred(sk27))),
inference(step,[status(thm)],[t22546,t306]) ).
cnf(t24196,plain,
trueq = leq(n2,succ(pred(sk27))),
inference(step,[status(thm)],[t24195,t1553]) ).
cnf(t24197,plain,
trueq = leq(n2,sk27),
inference(step,[status(thm)],[t24196,t358]) ).
cnf(t22576,plain,
leq(n2,sk27) = trueq,
inference(orient,[status(thm)],[t24197]) ).
cnf(t22585,plain,
trueq = ifeq(trueq,trueq,or(eq(n2,sk27),eq(gt(sk27,n2),trueq)),trueq),
inference(cp,[status(thm)],[t765,t22576]) ).
cnf(t24202,plain,
trueq = or(eq(n2,sk27),eq(gt(sk27,n2),trueq)),
inference(step,[status(thm)],[t22585,t306]) ).
cnf(c293,plain,
( pv5 != sk28
| n2 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(t182,plain,
or(not(eq(n2,sk27)),not(eq(pv5,sk28))) = trueq,
inference(equality_encoding,[status(esa)],[c293]) ).
cnf(t431,plain,
or(not(eq(n2,sk27)),not(eq(pv5,sk28))) = trueq,
inference(orient,[status(thm)],[t182]) ).
cnf(t22981,plain,
or(not(eq(n2,sk27)),not(eq(sk28,sk28))) = trueq,
inference(step,[status(thm)],[t431,t1418]) ).
cnf(t22982,plain,
or(not(eq(n2,sk27)),not(trueq)) = trueq,
inference(step,[status(thm)],[t22981,t360]) ).
cnf(t1430,plain,
or(not(eq(n2,sk27)),not(trueq)) = trueq,
inference(rw,[status(thm)],[t22982]) ).
cnf(t23255,plain,
or(not(eq(n2,sk27)),false) = trueq,
inference(step,[status(thm)],[t1430,t1540]) ).
cnf(t23256,plain,
not(eq(n2,sk27)) = trueq,
inference(step,[status(thm)],[t23255,t276]) ).
cnf(t3701,plain,
not(eq(n2,sk27)) = trueq,
inference(orient,[status(thm)],[t23256]) ).
cnf(t3702,plain,
false = ifeq(trueq,trueq,eq(n2,sk27),false),
inference(cp,[status(thm)],[t1539,t3701]) ).
cnf(t23257,plain,
false = eq(n2,sk27),
inference(step,[status(thm)],[t3702,t306]) ).
cnf(t3703,plain,
eq(n2,sk27) = false,
inference(orient,[status(thm)],[t23257]) ).
cnf(t24203,plain,
trueq = or(false,eq(gt(sk27,n2),trueq)),
inference(step,[status(thm)],[t24202,t3703]) ).
cnf(t24204,plain,
trueq = eq(gt(sk27,n2),trueq),
inference(step,[status(thm)],[t24203,t277]) ).
cnf(t22689,plain,
eq(gt(sk27,n2),trueq) = trueq,
inference(orient,[status(thm)],[t24204]) ).
cnf(t22690,plain,
trueq = ifeq(trueq,trueq,gt(sk27,n2),trueq),
inference(cp,[status(thm)],[t307,t22689]) ).
cnf(t24205,plain,
trueq = gt(sk27,n2),
inference(step,[status(thm)],[t22690,t306]) ).
cnf(t22693,plain,
gt(sk27,n2) = trueq,
inference(orient,[status(thm)],[t24205]) ).
cnf(t22701,plain,
trueq = ifeq(trueq,trueq,leq(n2,pred(sk27)),trueq),
inference(cp,[status(thm)],[t1160,t22693]) ).
cnf(t24206,plain,
trueq = leq(n2,pred(sk27)),
inference(step,[status(thm)],[t22701,t306]) ).
cnf(t22704,plain,
leq(n2,pred(sk27)) = trueq,
inference(orient,[status(thm)],[t24206]) ).
cnf(t22715,plain,
trueq = ifeq(trueq,trueq,leq(succ(n2),succ(pred(sk27))),trueq),
inference(cp,[status(thm)],[t803,t22704]) ).
cnf(t24207,plain,
trueq = leq(succ(n2),succ(pred(sk27))),
inference(step,[status(thm)],[t22715,t306]) ).
cnf(t24208,plain,
trueq = leq(n3,succ(pred(sk27))),
inference(step,[status(thm)],[t24207,t1574]) ).
cnf(t24209,plain,
trueq = leq(n3,sk27),
inference(step,[status(thm)],[t24208,t358]) ).
cnf(t22745,plain,
leq(n3,sk27) = trueq,
inference(orient,[status(thm)],[t24209]) ).
cnf(t22746,plain,
trueq = ifeq(trueq,trueq,leq(n3,n2),trueq),
inference(cp,[status(thm)],[t14053,t22745]) ).
cnf(t24210,plain,
trueq = leq(n3,n2),
inference(step,[status(thm)],[t22746,t306]) ).
cnf(t22783,plain,
leq(n3,n2) = trueq,
inference(orient,[status(thm)],[t24210]) ).
cnf(t24211,plain,
ifeq(trueq,trueq,false,trueq) = trueq,
inference(step,[status(thm)],[t4416,t22783]) ).
cnf(t24212,plain,
false = trueq,
inference(step,[status(thm)],[t24211,t306]) ).
cnf(t22823,plain,
false = trueq,
inference(rw,[status(thm)],[t24212]) ).
cnf(t22824,plain,
false = trueq,
inference(orient,[status(thm)],[t22823]) ).
fof(f51,axiom,
def != use,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defuse) ).
fof(f51_nnf,plain,
def != use,
inference(nnf_transformation,[status(thm)],[f51]) ).
fof(f51_sk,plain,
def != use,
inference(skolemisation,[status(esa)],[f51_nnf]) ).
cnf(c254,plain,
def != use,
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(c294,plain,
a_select3(z_defuse,sk27,sk28) != use,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(goal_0,negated_conjecture,
trueq != false,
inference(equality_encoding,[status(esa)],[c2,c254,c291,c292,c293,c294]) ).
cnf(g0_0,plain,
trueq != trueq,
inference(rw,[status(thm)],[goal_0,t22824]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV199+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 18:47:20 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 85.48/12.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 85.48/12.03 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------