%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV050+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 : Tue Sep 29 01:08:00 PM UTC 2026
% Result : Theorem 0.21s 1.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 18 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 33 ( 14 ~; 7 |; 10 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 15 con; 0-3 aty)
% Number of variables : 9 ( 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X0] : sum(n0,tptp_minus_1,X0) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_plus_base) ).
fof(f28,axiom,
succ(tptp_minus_1) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
fof(f30,axiom,
! [X0] : plus(n1,X0) = succ(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_1_l) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_minus_1) ).
fof(f40,axiom,
! [X0] : pred(succ(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_succ) ).
fof(f53,conjecture,
( ( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) )
=> ( n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0022) ).
fof(f54,negated_conjecture,
~ ( ( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) )
=> ( n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f87,plain,
( ( n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| pv86 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| pv88 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) )
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ),
inference(ennf_transformation,[],[f54]) ).
fof(f88,plain,
( ( n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| pv86 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| pv88 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) )
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ),
inference(flattening,[],[f87]) ).
fof(f114,plain,
pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))),
inference(cnf_transformation,[],[f88]) ).
fof(f115,plain,
pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))),
inference(cnf_transformation,[],[f88]) ).
fof(f116,plain,
( n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| pv86 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| pv88 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ),
inference(cnf_transformation,[],[f88]) ).
fof(f117,plain,
! [X0] : n0 = sum(n0,tptp_minus_1,X0),
inference(cnf_transformation,[],[f26]) ).
fof(f129,plain,
! [X0] : succ(X0) = plus(n1,X0),
inference(cnf_transformation,[],[f30]) ).
fof(f139,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f146,plain,
n0 = succ(tptp_minus_1),
inference(cnf_transformation,[],[f28]) ).
fof(f178,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[],[f40]) ).
fof(f192,plain,
n0 = plus(n1,tptp_minus_1),
inference(definition_unfolding,[],[f146,f129]) ).
fof(f204,plain,
! [X0] : minus(plus(n1,X0),n1) = X0,
inference(definition_unfolding,[],[f178,f139,f129]) ).
fof(f219,plain,
tptp_minus_1 = minus(n0,n1),
inference(superposition,[],[f204,f192]) ).
fof(f221,plain,
( n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| pv88 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ),
inference(forward_subsumption_resolution,[],[f116,f115]) ).
fof(f222,plain,
n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))),
inference(forward_subsumption_resolution,[],[f221,f114]) ).
fof(f249,plain,
n0 != sum(n0,tptp_minus_1,divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))),
inference(superposition,[],[f222,f219]) ).
fof(f253,plain,
$false,
inference(forward_subsumption_resolution,[],[f249,f117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV050+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n013.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 09:46:36 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/1.30 % (1061065)Detected formulas, will run a generic FOF schedule.
% 0.21/1.30 % (1061073)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3245289397:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.21/1.30 % (1061073)Refutation not found, incomplete strategy
% 0.21/1.30 % (1061073)------------------------------
% 0.21/1.30 % (1061073)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (1061073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (1061073)CaDiCaL version: 2.1.3
% 0.21/1.30 % (1061073)Termination reason: Refutation not found, incomplete strategy
% 0.21/1.30 % (1061073)Time elapsed: 0.002 s
% 0.21/1.30 % (1061073)Peak memory usage: 88 MB
% 0.21/1.30 % (1061073)Instructions burned: 4 (million)
% 0.21/1.30 % (1061070)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4010944492:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.21/1.30 % (1061071)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1309568145:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.21/1.30 % (1061072)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3664855236:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.21/1.30 % (1061076)dis-21_1_sil=8000:lcm=predicate:random_seed=324025293:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.21/1.30 % (1061075)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=684405140:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.21/1.30 % (1061074)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3301767990:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.21/1.30 % (1061074)First to succeed.
% 0.21/1.30 % (1061074)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1061065"
% 0.21/1.30 % (1061075)Also succeeded, but the first one will report.
% 0.21/1.30 % (1061076)Instruction limit reached!
% 0.21/1.30 % (1061076)------------------------------
% 0.21/1.30 % (1061076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (1061076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (1061076)CaDiCaL version: 2.1.3
% 0.21/1.30 % (1061076)Termination reason: Instruction limit
% 0.21/1.30 % (1061076)Termination phase: Saturation
% 0.21/1.30 % (1061076)Time elapsed: 0.066 s
% 0.21/1.30 % (1061076)Peak memory usage: 88 MB
% 0.21/1.30 % (1061076)Instructions burned: 131 (million)
% 0.21/1.30 % (1061073)------------------------------
% 0.21/1.30 % (1061073)------------------------------
% 0.21/1.30 % (1061084)lrs+10_1_sil=8000:sp=occurrence:random_seed=3266172671:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.21/1.30 % (1061085)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3712933356:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.21/1.30 % (1061084)Also succeeded, but the first one will report.
% 0.21/1.30 % (1061074)Refutation found. Thanks to Tanya!
% 0.21/1.30 % SZS status Theorem for theBenchmark
% 0.21/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.30 % (1061074)------------------------------
% 0.21/1.30 % (1061074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.30 % (1061074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.30 % (1061074)CaDiCaL version: 2.1.3
% 0.21/1.30 % (1061074)Termination reason: Refutation
% 0.21/1.30 % (1061074)Time elapsed: 0.006 s
% 0.21/1.30 % (1061074)Peak memory usage: 88 MB
% 0.21/1.30 % (1061074)Instructions burned: 8 (million)
% 0.21/1.30 % (1061074)------------------------------
% 0.21/1.30 % (1061074)------------------------------
% 0.21/1.30 % (1061065)Success in time 0.446 s
% 0.21/1.30 % Vampire exiting
%------------------------------------------------------------------------------