%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN083+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 01:49:37 PM UTC 2026
% Result : Theorem 3.59s 1.20s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 1 def)
% Number of atoms : 12 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 14 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] : f(X0,f(X1,X2)) = f(f(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p61_1) ).
fof(f2,conjecture,
! [X0,X1,X2,X3] : f(X0,f(X1,f(X2,X3))) = f(f(f(X0,X1),X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel61) ).
fof(f3,negated_conjecture,
~ ! [X0,X1,X2,X3] : f(X0,f(X1,f(X2,X3))) = f(f(f(X0,X1),X2),X3),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
? [X0,X1,X2,X3] : f(X0,f(X1,f(X2,X3))) != f(f(f(X0,X1),X2),X3),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
f(sK0,f(sK1,f(sK2,sK3))) != f(f(f(sK0,sK1),sK2),sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f4]) ).
fof(f6,plain,
f(sK0,f(sK1,f(sK2,sK3))) != f(f(f(sK0,sK1),sK2),sK3),
inference(cnf_transformation,[],[f5]) ).
fof(f7,plain,
! [X2,X0,X1] : f(X0,f(X1,X2)) = f(f(X0,X1),X2),
inference(cnf_transformation,[],[f1]) ).
fof(f8,definition,
~ sP4(f(sK0,f(sK1,f(sK2,sK3)))),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f9,plain,
sP4(f(f(f(sK0,sK1),sK2),sK3)),
inference(inequality_splitting,[],[f6,f8]) ).
fof(f10,plain,
sP4(f(f(sK0,sK1),f(sK2,sK3))),
inference(forward_demodulation,[],[f9,f7]) ).
fof(f11,plain,
sP4(f(sK0,f(sK1,f(sK2,sK3)))),
inference(forward_demodulation,[],[f10,f7]) ).
fof(f12,plain,
$false,
inference(forward_subsumption_resolution,[],[f11,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN083+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n010.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 15:32:33 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.59/1.20 % (2007564)Detected formulas, will run a generic FOF schedule.
% 3.59/1.20 % (2007575)dis-21_1_sil=8000:lcm=predicate:random_seed=1379814643: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)
% 3.59/1.20 % (2007575)Refutation not found, incomplete strategy
% 3.59/1.20 % (2007575)------------------------------
% 3.59/1.20 % (2007575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.20 % (2007575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.20 % (2007575)CaDiCaL version: 2.1.3
% 3.59/1.20 % (2007575)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.20 % (2007575)Time elapsed: 0.001 s
% 3.59/1.20 % (2007575)Peak memory usage: 88 MB
% 3.59/1.20 % (2007570)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=397765133:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.59/1.20 % (2007571)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=3379346228:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.59/1.20 % (2007569)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=3701923696:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.59/1.20 % (2007573)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3832388284:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.59/1.20 % (2007572)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4179600707:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.59/1.20 % (2007574)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2261859034:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.59/1.20 % (2007572)First to succeed.
% 3.59/1.20 % (2007573)Also succeeded, but the first one will report.
% 3.59/1.20 % (2007574)Also succeeded, but the first one will report.
% 3.59/1.20 % (2007572)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2007564"
% 3.59/1.20 % (2007575)------------------------------
% 3.59/1.20 % (2007575)------------------------------
% 3.59/1.20 % (2007583)lrs+10_1_sil=8000:sp=occurrence:random_seed=7650767:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.59/1.20 % (2007583)Also succeeded, but the first one will report.
% 3.59/1.20 % (2007572)Refutation found. Thanks to Tanya!
% 3.59/1.20 % SZS status Theorem for theBenchmark
% 3.59/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.20 % (2007572)------------------------------
% 3.68/1.20 % (2007572)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.20 % (2007572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.20 % (2007572)CaDiCaL version: 2.1.3
% 3.68/1.20 % (2007572)Termination reason: Refutation
% 3.68/1.20 % (2007572)Time elapsed: 0.001 s
% 3.68/1.20 % (2007572)Peak memory usage: 88 MB
% 3.68/1.20 % (2007572)------------------------------
% 3.68/1.20 % (2007572)------------------------------
% 3.68/1.20 % (2007564)Success in time 0.433 s
% 3.68/1.20 % Vampire exiting
%------------------------------------------------------------------------------