%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW252+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 01:29:56 PM UTC 2026
% Result : ContradictoryAxioms 11.37s 2.72s
% Output : Refutation 11.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-4 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,axiom,
! [X0] : X0 != hAPP(c_Nat_OSuc,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(f597,axiom,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(f1250,axiom,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(c_COMBB(X5,X4,X3,X2),X1),X0) = hAPP(X2,hAPP(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(f1252,axiom,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X5,X4,X3),X2),X1),X0) = hAPP(hAPP(X2,X0),hAPP(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(f2837,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
inference(cnf_transformation,[],[f27]) ).
fof(f3654,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[],[f597]) ).
fof(f4469,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(c_COMBB(X5,X4,X3,X2),X1),X0) = hAPP(X2,hAPP(X1,X0)),
inference(cnf_transformation,[],[f1250]) ).
fof(f4471,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X5,X4,X3),X2),X1),X0) = hAPP(hAPP(X2,X0),hAPP(X1,X0)),
inference(cnf_transformation,[],[f1252]) ).
fof(f4829,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),c_COMBB(X3,X4,X5,X6)),X7),X8) = hAPP(X6,hAPP(X8,hAPP(X7,X8))),
inference(superposition,[],[f4469,f4471]) ).
fof(f4861,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(X7,hAPP(X6,X7)) != hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),c_COMBB(X3,X4,X5,c_Nat_OSuc)),X6),X7),
inference(superposition,[],[f2837,f4829]) ).
fof(f5012,plain,
! [X2,X3,X0,X1,X6,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),c_COMBB(X4,X5,X6,c_Nat_OSuc)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) != hAPP(X0,X0),
inference(superposition,[],[f4861,f3654]) ).
fof(f5026,plain,
$false,
inference(equality_resolution,[],[f5012]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW252+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.26 % Computer : n011.cluster.edu
% 0.09/0.26 % Model : x86_64 x86_64
% 0.09/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.26 % Memory : 8046.5625MB
% 0.09/0.26 % OS : Linux 6.8.0-71-generic
% 0.09/0.26 % CPULimit : 300
% 0.09/0.26 % WCLimit : 300
% 0.09/0.26 % DateTime : Mon Sep 28 13:24:39 UTC 2026
% 0.09/0.27 % CPUTime :
% 0.09/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.32 Running first-order theorem proving
% 0.25/0.32 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
% 11.37/2.71 % (3380759)Detected formulas, will run a generic FOF schedule.
% 11.37/2.71 % (3380765)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=1436470659:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.37/2.71 % (3380768)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3622924852:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.37/2.71 % (3380764)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=661349264:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.37/2.71 % (3380767)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=136949318:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.37/2.71 % (3380766)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=4282388499:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.37/2.71 % (3380769)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2626319202:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.37/2.71 % (3380770)dis-21_1_sil=8000:lcm=predicate:random_seed=739193005: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)
% 11.37/2.71 % (3380767)Refutation not found, incomplete strategy
% 11.37/2.71 % (3380767)------------------------------
% 11.37/2.71 % (3380767)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.37/2.71 % (3380767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.37/2.71 % (3380767)CaDiCaL version: 2.1.3
% 11.37/2.71 % (3380767)Termination reason: Refutation not found, incomplete strategy
% 11.37/2.71 % (3380767)Time elapsed: 0.039 s
% 11.37/2.71 % (3380767)Peak memory usage: 90 MB
% 11.37/2.71 % (3380767)Instructions burned: 39 (million)
% 11.37/2.71 % (3380768)Instruction limit reached!
% 11.37/2.71 % (3380768)------------------------------
% 11.37/2.71 % (3380768)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.37/2.71 % (3380768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.37/2.71 % (3380768)CaDiCaL version: 2.1.3
% 11.37/2.71 % (3380768)Termination reason: Instruction limit
% 11.37/2.71 % (3380768)Termination phase: Saturation
% 11.37/2.71 % (3380768)Time elapsed: 0.111 s
% 11.37/2.71 % (3380768)Peak memory usage: 90 MB
% 11.37/2.71 % (3380768)Instructions burned: 119 (million)
% 11.37/2.71 % (3380770)Instruction limit reached!
% 11.37/2.71 % (3380770)------------------------------
% 11.37/2.71 % (3380770)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.37/2.71 % (3380770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.37/2.71 % (3380770)CaDiCaL version: 2.1.3
% 11.37/2.71 % (3380770)Termination reason: Instruction limit
% 11.37/2.71 % (3380770)Termination phase: Saturation
% 11.37/2.71 % (3380770)Time elapsed: 0.111 s
% 11.37/2.71 % (3380770)Peak memory usage: 90 MB
% 11.37/2.71 % (3380770)Instructions burned: 129 (million)
% 11.37/2.71 % (3380769)Instruction limit reached!
% 11.37/2.71 % (3380769)------------------------------
% 11.37/2.71 % (3380769)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.37/2.72 % (3380769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.37/2.72 % (3380769)CaDiCaL version: 2.1.3
% 11.37/2.72 % (3380769)Termination reason: Instruction limit
% 11.37/2.72 % (3380769)Termination phase: Saturation
% 11.37/2.72 % (3380769)Time elapsed: 0.117 s
% 11.37/2.72 % (3380769)Peak memory usage: 90 MB
% 11.37/2.72 % (3380769)Instructions burned: 139 (million)
% 11.37/2.72 % (3380778)lrs+10_1_sil=8000:sp=occurrence:random_seed=2007012752:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 11.37/2.72 % (3380780)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1032421694:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 11.37/2.72 % (3380779)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1062812330:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 11.37/2.72 % (3380767)------------------------------
% 11.37/2.72 % (3380767)------------------------------
% 11.37/2.72 % (3380779)Instruction limit reached!
% 11.37/2.72 % (3380779)------------------------------
% 11.37/2.72 % (3380779)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.37/2.72 % (3380779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.37/2.72 % (3380779)CaDiCaL version: 2.1.3
% 11.37/2.72 % (3380779)Termination reason: Instruction limit
% 11.37/2.72 % (3380779)Termination phase: Saturation
% 11.37/2.72 % (3380779)Time elapsed: 0.143 s
% 11.37/2.72 % (3380779)Peak memory usage: 90 MB
% 11.37/2.72 % (3380779)Instructions burned: 157 (million)
% 11.37/2.72 % (3380778)Instruction limit reached!
% 11.37/2.72 % (3380778)------------------------------
% 11.37/2.72 % (3380778)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.37/2.72 % (3380778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.37/2.72 % (3380778)CaDiCaL version: 2.1.3
% 11.37/2.72 % (3380778)Termination reason: Instruction limit
% 11.37/2.72 % (3380778)Termination phase: Saturation
% 11.37/2.72 % (3380778)Time elapsed: 0.256 s
% 11.37/2.72 % (3380778)Peak memory usage: 92 MB
% 11.37/2.72 % (3380778)Instructions burned: 285 (million)
% 11.37/2.72 % (3380780)Instruction limit reached!
% 11.37/2.72 % (3380780)------------------------------
% 11.37/2.72 % (3380780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.37/2.72 % (3380780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.37/2.72 % (3380780)CaDiCaL version: 2.1.3
% 11.37/2.72 % (3380780)Termination reason: Instruction limit
% 11.37/2.72 % (3380780)Termination phase: Saturation
% 11.37/2.72 % (3380780)Time elapsed: 0.322 s
% 11.37/2.72 % (3380780)Peak memory usage: 92 MB
% 11.37/2.72 % (3380780)Instructions burned: 325 (million)
% 11.37/2.72 % (3380784)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2044896530:s2a=on:i=248:s2at=1.23:gtg=position_2992 on theBenchmark for (2992ds/248Mi)
% 11.37/2.72 % (3380785)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2172582393:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2991 on theBenchmark for (2991ds/294Mi)
% 11.37/2.72 % (3380786)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2487715349:i=2350_2991 on theBenchmark for (2991ds/2350Mi)
% 11.37/2.72 % (3380765)First to succeed.
% 11.37/2.72 % (3380765)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3380759"
% 11.37/2.72 % (3380785)Refutation not found, incomplete strategy
% 11.37/2.72 % (3380785)------------------------------
% 11.37/2.72 % (3380785)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.37/2.72 % (3380785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.37/2.72 % (3380785)CaDiCaL version: 2.1.3
% 11.37/2.72 % (3380785)Termination reason: Refutation not found, incomplete strategy
% 11.37/2.72 % (3380785)Time elapsed: 0.121 s
% 11.37/2.72 % (3380785)Peak memory usage: 91 MB
% 11.37/2.72 % (3380785)Instructions burned: 135 (million)
% 11.37/2.72 % (3380784)Instruction limit reached!
% 11.37/2.72 % (3380784)------------------------------
% 11.37/2.72 % (3380784)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.37/2.72 % (3380784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.37/2.72 % (3380784)CaDiCaL version: 2.1.3
% 11.37/2.72 % (3380784)Termination reason: Instruction limit
% 11.37/2.72 % (3380784)Termination phase: Saturation
% 11.37/2.72 % (3380784)Time elapsed: 0.243 s
% 11.37/2.72 % (3380784)Peak memory usage: 92 MB
% 11.37/2.72 % (3380784)Instructions burned: 249 (million)
% 11.37/2.72 % (3380788)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=452444693:cts=off:i=113:fsr=off:ss=included:sgt=4_2989 on theBenchmark for (2989ds/113Mi)
% 11.37/2.72 % (3380788)Instruction limit reached!
% 11.37/2.72 % (3380788)------------------------------
% 11.37/2.72 % (3380788)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.37/2.72 % (3380788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.37/2.72 % (3380788)CaDiCaL version: 2.1.3
% 11.37/2.72 % (3380788)Termination reason: Instruction limit
% 11.37/2.72 % (3380788)Termination phase: Saturation
% 11.37/2.72 % (3380788)Time elapsed: 0.105 s
% 11.37/2.72 % (3380788)Peak memory usage: 90 MB
% 11.37/2.72 % (3380788)Instructions burned: 114 (million)
% 11.37/2.72 % (3380765)Refutation found. Thanks to Tanya!
% 11.37/2.72 % SZS status ContradictoryAxioms for theBenchmark
% 11.37/2.72 % SZS output start Proof for theBenchmark
% See solution above
% 11.37/2.72 % (3380765)------------------------------
% 11.37/2.72 % (3380765)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.37/2.72 % (3380765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.37/2.72 % (3380765)CaDiCaL version: 2.1.3
% 11.37/2.72 % (3380765)Termination reason: Refutation
% 11.37/2.72 % (3380765)Time elapsed: 0.987 s
% 11.37/2.72 % (3380765)Peak memory usage: 150 MB
% 11.37/2.72 % (3380765)Instructions burned: 1840 (million)
% 11.37/2.72 % (3380765)------------------------------
% 11.37/2.72 % (3380765)------------------------------
% 11.37/2.72 % (3380759)Success in time 1.532 s
% 11.37/2.72 % Vampire exiting
%------------------------------------------------------------------------------