%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX206+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 01:46:10 PM UTC 2026
% Result : Theorem 3.66s 1.28s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 9 unt; 1 def)
% Number of atoms : 11 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 4 ~; 0 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 10 ( 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : x2(z,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
fof(f5,conjecture,
? [X0] : x2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_005) ).
fof(f6,negated_conjecture,
~ ? [X0] : x2(X0,X0) = X0,
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
! [X0] : x2(X0,X0) != X0,
inference(ennf_transformation,[],[f6]) ).
fof(f10,plain,
! [X0] : x2(z,X0) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f12,plain,
! [X0] : x2(X0,X0) != X0,
inference(cnf_transformation,[],[f7]) ).
fof(f13,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f16,plain,
! [X0] : sQ0_eqProxy(x2(z,X0),X0),
inference(equality_proxy_replacement,[],[f10,f13]) ).
fof(f18,plain,
! [X0] : ~ sQ0_eqProxy(x2(X0,X0),X0),
inference(equality_proxy_replacement,[],[f12,f13]) ).
fof(f21,plain,
$false,
inference(resolution,[],[f16,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX206+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n007.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 15:07:54 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 3.66/1.28 % (2485486)Detected formulas, will run a generic FOF schedule.
% 3.66/1.28 % (2485493)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=390419193:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.66/1.28 % (2485494)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=599735201:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.66/1.28 % (2485495)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2796081589:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.66/1.28 % (2485497)dis-21_1_sil=8000:lcm=predicate:random_seed=3510878428: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)
% 3.66/1.28 % (2485491)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=149137954:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.66/1.28 % (2485492)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=572033361:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.66/1.28 % (2485496)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1130990352:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.66/1.28 % (2485497)First to succeed.
% 3.66/1.28 % (2485496)Also succeeded, but the first one will report.
% 3.66/1.28 % (2485497)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2485486"
% 3.66/1.28 % (2485494)Instruction limit reached!
% 3.66/1.28 % (2485494)------------------------------
% 3.66/1.28 % (2485494)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.28 % (2485494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.28 % (2485494)CaDiCaL version: 2.1.3
% 3.66/1.28 % (2485494)Termination reason: Instruction limit
% 3.66/1.28 % (2485494)Termination phase: Saturation
% 3.66/1.28 % (2485494)Time elapsed: 0.047 s
% 3.66/1.28 % (2485494)Peak memory usage: 88 MB
% 3.66/1.28 % (2485494)Instructions burned: 111 (million)
% 3.66/1.28 % (2485495)Instruction limit reached!
% 3.66/1.28 % (2485495)------------------------------
% 3.66/1.28 % (2485495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.28 % (2485495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.28 % (2485495)CaDiCaL version: 2.1.3
% 3.66/1.28 % (2485495)Termination reason: Instruction limit
% 3.66/1.28 % (2485495)Termination phase: Saturation
% 3.66/1.28 % (2485495)Time elapsed: 0.051 s
% 3.66/1.28 % (2485495)Peak memory usage: 87 MB
% 3.66/1.28 % (2485495)Instructions burned: 120 (million)
% 3.66/1.28 % (2485505)lrs+10_1_sil=8000:sp=occurrence:random_seed=1231627043:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.66/1.28 % (2485505)Also succeeded, but the first one will report.
% 3.66/1.28 % (2485506)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2587287599:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.66/1.28 % (2485506)Also succeeded, but the first one will report.
% 3.66/1.28 % (2485497)Refutation found. Thanks to Tanya!
% 3.66/1.28 % SZS status Theorem for theBenchmark
% 3.66/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.28 % (2485497)------------------------------
% 3.66/1.28 % (2485497)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.28 % (2485497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.28 % (2485497)CaDiCaL version: 2.1.3
% 3.66/1.28 % (2485497)Termination reason: Refutation
% 3.66/1.28 % (2485497)Time elapsed: 0.001 s
% 3.66/1.28 % (2485497)Peak memory usage: 88 MB
% 3.66/1.28 % (2485497)------------------------------
% 3.66/1.28 % (2485497)------------------------------
% 3.66/1.28 % (2485486)Success in time 0.435 s
% 3.66/1.28 % Vampire exiting
%------------------------------------------------------------------------------