%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN353-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 01:50:20 PM UTC 2026
% Result : Unsatisfiable 3.46s 1.17s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 13
% Syntax : Number of formulae : 53 ( 4 unt; 0 def)
% Number of atoms : 146 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 169 ( 76 ~; 93 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-3 aty)
% Number of variables : 110 ( 110 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] :
( ~ f(a,a,z(X0,X1,X2))
| ~ f(X0,X1,X2)
| f(X1,X2,X0)
| f(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
fof(f2,negated_conjecture,
! [X2,X0,X1] :
( ~ f(X2,X1,z(X1,X2,X0))
| f(X1,X2,X0)
| ~ f(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
fof(f3,negated_conjecture,
! [X2,X0,X1] :
( ~ f(X2,X1,z(X1,X2,X0))
| f(X2,X0,X1)
| ~ f(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
fof(f4,negated_conjecture,
! [X2,X0,X1] :
( f(X2,X1,z(X1,X2,X0))
| f(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
fof(f5,negated_conjecture,
! [X2,X0,X1] :
( f(X1,X0,z(X0,X1,X2))
| ~ f(X1,X2,X0)
| ~ f(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
fof(f6,negated_conjecture,
! [X2,X0,X1] :
( ~ f(X2,z(X2,X0,X1),X0)
| f(X2,X0,X1)
| ~ f(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
fof(f7,negated_conjecture,
! [X2,X0,X1] :
( ~ f(X2,z(X2,X0,X1),X0)
| f(X1,X2,X0)
| ~ f(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause7) ).
fof(f8,negated_conjecture,
! [X2,X0,X1] :
( f(X2,z(X2,X0,X1),X0)
| f(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f10,negated_conjecture,
! [X2,X0,X1] :
( ~ f(z(X1,X2,X0),X2,X1)
| f(X1,X2,X0)
| f(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause10) ).
fof(f11,negated_conjecture,
! [X2,X0,X1] :
( ~ f(z(X2,X0,X1),X0,X2)
| f(X2,X0,X1)
| f(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause11) ).
fof(f12,negated_conjecture,
! [X2,X0,X1] :
( f(z(X1,X2,X0),X2,X1)
| ~ f(X2,X0,X1)
| ~ f(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause12) ).
fof(f13,negated_conjecture,
! [X2,X0,X1] :
( f(z(X0,X1,X2),X1,X0)
| ~ f(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause13) ).
fof(f17,negated_conjecture,
! [X2,X0,X1] :
( ~ f(z(X0,X1,X2),z(X0,X1,X2),z(X0,X1,X2))
| ~ f(X1,X2,X0)
| ~ f(X2,X0,X1)
| ~ f(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause17) ).
fof(f31,plain,
! [X0] :
( ~ f(a,a,X0)
| f(a,X0,a)
| f(X0,a,a)
| f(X0,a,a) ),
inference(resolution,[],[f1,f4]) ).
fof(f32,plain,
! [X0] :
( f(a,X0,a)
| ~ f(a,a,X0)
| f(X0,a,a) ),
inference(duplicate_literal_removal,[],[f31]) ).
fof(f35,plain,
! [X0] :
( ~ f(a,a,z(a,a,X0))
| f(z(a,a,X0),a,a)
| f(a,a,X0)
| ~ f(a,X0,a) ),
inference(resolution,[],[f32,f6]) ).
fof(f36,plain,
! [X0] :
( f(z(a,a,X0),a,a)
| ~ f(a,a,z(a,a,X0))
| ~ f(a,X0,a) ),
inference(forward_subsumption_resolution,[],[f35,f13]) ).
fof(f42,plain,
! [X0] :
( ~ f(a,a,z(a,a,X0))
| ~ f(a,X0,a)
| f(a,a,X0)
| f(X0,a,a) ),
inference(resolution,[],[f36,f10]) ).
fof(f43,plain,
! [X0] :
( ~ f(a,a,z(a,a,X0))
| ~ f(a,X0,a)
| f(a,a,X0) ),
inference(forward_subsumption_resolution,[],[f42,f2]) ).
fof(f45,plain,
! [X0] :
( f(a,a,X0)
| ~ f(a,X0,a)
| f(X0,a,a) ),
inference(resolution,[],[f43,f4]) ).
fof(f49,plain,
! [X0] :
( ~ f(a,z(a,a,X0),a)
| f(z(a,a,X0),a,a)
| f(a,X0,a)
| ~ f(X0,a,a) ),
inference(resolution,[],[f45,f3]) ).
fof(f52,plain,
! [X0] :
( f(z(a,a,X0),a,a)
| f(a,X0,a)
| ~ f(X0,a,a) ),
inference(forward_subsumption_resolution,[],[f49,f8]) ).
fof(f53,plain,
! [X0] :
( f(z(a,a,X0),a,a)
| ~ f(X0,a,a) ),
inference(forward_subsumption_resolution,[],[f52,f12]) ).
fof(f54,plain,
! [X0] :
( f(a,a,X0)
| ~ f(X0,a,a)
| f(a,X0,a) ),
inference(resolution,[],[f53,f11]) ).
fof(f57,plain,
! [X0] :
( ~ f(z(a,a,X0),a,a)
| f(a,z(a,a,X0),a)
| ~ f(a,X0,a)
| f(a,a,X0) ),
inference(resolution,[],[f54,f43]) ).
fof(f61,plain,
! [X0] :
( ~ f(z(a,a,X0),a,a)
| ~ f(a,X0,a)
| f(a,a,X0) ),
inference(forward_subsumption_resolution,[],[f57,f6]) ).
fof(f62,plain,
! [X0] :
( ~ f(z(a,a,X0),a,a)
| f(a,a,X0) ),
inference(forward_subsumption_resolution,[],[f61,f11]) ).
fof(f67,plain,
! [X0] :
( f(a,a,X0)
| ~ f(X0,a,a) ),
inference(resolution,[],[f62,f53]) ).
fof(f75,plain,
! [X0] :
( ~ f(z(a,a,X0),a,a)
| f(a,X0,a)
| ~ f(X0,a,a) ),
inference(resolution,[],[f67,f3]) ).
fof(f77,plain,
! [X0] :
( f(a,X0,a)
| ~ f(X0,a,a) ),
inference(forward_subsumption_resolution,[],[f75,f53]) ).
fof(f81,plain,
! [X0] :
( ~ f(z(a,a,X0),a,a)
| f(X0,a,a)
| ~ f(a,X0,a) ),
inference(resolution,[],[f77,f7]) ).
fof(f87,plain,
! [X0] :
( f(X0,a,a)
| ~ f(a,X0,a)
| ~ f(a,a,X0) ),
inference(resolution,[],[f81,f13]) ).
fof(f91,plain,
! [X0] :
( f(X0,a,a)
| ~ f(a,a,X0) ),
inference(forward_subsumption_resolution,[],[f87,f32]) ).
fof(f117,plain,
! [X0] :
( ~ f(a,a,z(a,a,X0))
| f(a,a,X0) ),
inference(resolution,[],[f91,f62]) ).
fof(f132,plain,
! [X0] :
( f(a,a,X0)
| f(X0,a,a) ),
inference(resolution,[],[f117,f4]) ).
fof(f133,plain,
! [X0] : f(a,a,X0),
inference(forward_subsumption_resolution,[],[f132,f67]) ).
fof(f134,plain,
! [X2,X0,X1] :
( f(X2,X0,X1)
| f(X1,X2,X0)
| ~ f(X0,X1,X2) ),
inference(resolution,[],[f133,f1]) ).
fof(f139,plain,
! [X2,X0,X1] :
( f(z(X0,X1,X2),X1,X0)
| ~ f(X0,z(X0,X1,X2),X1)
| f(X1,X2,X0)
| ~ f(X2,X0,X1) ),
inference(resolution,[],[f134,f3]) ).
fof(f142,plain,
! [X2,X0,X1] :
( f(X0,X1,z(X1,X0,X2))
| ~ f(z(X1,X0,X2),X0,X1)
| f(X1,X0,X2)
| ~ f(X0,X2,X1) ),
inference(resolution,[],[f134,f6]) ).
fof(f155,plain,
! [X2,X0,X1] :
( f(X0,X1,z(X1,X0,X2))
| ~ f(z(X1,X0,X2),X0,X1)
| ~ f(X0,X2,X1) ),
inference(forward_subsumption_resolution,[],[f142,f5]) ).
fof(f157,plain,
! [X2,X0,X1] :
( f(z(X0,X1,X2),X1,X0)
| f(X1,X2,X0)
| ~ f(X2,X0,X1) ),
inference(forward_subsumption_resolution,[],[f139,f8]) ).
fof(f158,plain,
! [X2,X0,X1] :
( f(z(X0,X1,X2),X1,X0)
| ~ f(X2,X0,X1) ),
inference(forward_subsumption_resolution,[],[f157,f12]) ).
fof(f181,plain,
! [X2,X0,X1] :
( ~ f(z(X0,X1,X2),X1,X0)
| ~ f(X1,X2,X0)
| f(X0,X1,X2)
| ~ f(X2,X0,X1) ),
inference(resolution,[],[f155,f2]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ f(z(X0,X1,X2),X1,X0)
| f(X0,X1,X2)
| ~ f(X2,X0,X1) ),
inference(forward_subsumption_resolution,[],[f181,f134]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ f(z(X0,X1,X2),X1,X0)
| f(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f187,f10]) ).
fof(f190,plain,
! [X2,X0,X1] :
( f(X0,X1,X2)
| ~ f(X2,X0,X1) ),
inference(resolution,[],[f189,f158]) ).
fof(f206,plain,
! [X2,X0,X1] :
( ~ f(X0,z(X0,X1,X2),X1)
| f(X0,X1,X2)
| f(X1,X2,X0) ),
inference(resolution,[],[f190,f11]) ).
fof(f217,plain,
! [X2,X0,X1] :
( ~ f(X0,z(X0,X1,X2),X1)
| f(X1,X2,X0) ),
inference(forward_subsumption_resolution,[],[f206,f190]) ).
fof(f219,plain,
! [X2,X0,X1] : f(X1,X2,X0),
inference(forward_subsumption_resolution,[],[f217,f8]) ).
fof(f228,plain,
! [X2,X0,X1] :
( ~ f(X0,X1,X2)
| ~ f(X1,X2,X0)
| ~ f(X2,X0,X1) ),
inference(resolution,[],[f219,f17]) ).
fof(f236,plain,
! [X2,X0,X1] :
( ~ f(X1,X2,X0)
| ~ f(X2,X0,X1) ),
inference(forward_subsumption_resolution,[],[f228,f190]) ).
fof(f237,plain,
! [X2,X0,X1] : ~ f(X1,X2,X0),
inference(forward_subsumption_resolution,[],[f236,f190]) ).
fof(f238,plain,
$false,
inference(forward_subsumption_resolution,[],[f237,f219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN353-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n010.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 15:48:03 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
% 3.46/1.17 % (2028954)Input is clausal, will run a generic CNF schedule.
% 3.46/1.17 % (2028961)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=550497977:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.46/1.17 % (2028962)lrs+10_1_sil=8000:sp=occurrence:random_seed=1119173718:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.46/1.17 % (2028965)dis-21_1_sil=8000:lcm=predicate:random_seed=3345367388:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.46/1.17 % (2028963)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3598002801:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.46/1.17 % (2028959)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=739884759:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.46/1.17 % (2028960)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1656852632:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.46/1.17 % (2028964)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1041025565:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.46/1.17 % (2028963)First to succeed.
% 3.46/1.17 % (2028962)Also succeeded, but the first one will report.
% 3.46/1.17 % (2028963)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2028954"
% 3.46/1.17 % (2028965)Also succeeded, but the first one will report.
% 3.46/1.17 % (2028964)Instruction limit reached!
% 3.46/1.17 % (2028964)------------------------------
% 3.46/1.17 % (2028964)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.17 % (2028964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.17 % (2028964)CaDiCaL version: 2.1.3
% 3.46/1.17 % (2028964)Termination reason: Instruction limit
% 3.46/1.17 % (2028964)Termination phase: Saturation
% 3.46/1.17 % (2028964)Time elapsed: 0.101 s
% 3.46/1.17 % (2028964)Peak memory usage: 88 MB
% 3.46/1.17 % (2028964)Instructions burned: 181 (million)
% 3.46/1.17 % (2028973)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1852830617:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.46/1.17 % (2028973)Also succeeded, but the first one will report.
% 3.46/1.17 % (2028963)Refutation found. Thanks to Tanya!
% 3.46/1.17 % SZS status Unsatisfiable for theBenchmark
% 3.46/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.17 % (2028963)------------------------------
% 3.46/1.17 % (2028963)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.17 % (2028963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.17 % (2028963)CaDiCaL version: 2.1.3
% 3.46/1.17 % (2028963)Termination reason: Refutation
% 3.46/1.17 % (2028963)Time elapsed: 0.006 s
% 3.46/1.17 % (2028963)Peak memory usage: 88 MB
% 3.46/1.17 % (2028963)Instructions burned: 8 (million)
% 3.46/1.17 % (2028963)------------------------------
% 3.46/1.17 % (2028963)------------------------------
% 3.46/1.17 % (2028954)Success in time 0.413 s
% 3.46/1.17 % Vampire exiting
%------------------------------------------------------------------------------