%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP184-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 10:13:15 AM UTC 2026
% Result : Unsatisfiable 11.36s 2.57s
% Output : Refutation 11.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 63 ( 63 unt; 5 def)
% Number of atoms : 63 ( 62 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
fof(f14,axiom,
! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb1) ).
fof(f15,axiom,
! [X2,X0,X1] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
fof(f16,axiom,
! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
fof(f17,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p21) ).
fof(f18,definition,
sF0 = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f19,plain,
least_upper_bound(a,identity) = sF0,
inference(reorient_equations,[],[f18]) ).
fof(f20,definition,
sF1 = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f21,plain,
greatest_lower_bound(a,identity) = sF1,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF2 = inverse(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f23,plain,
inverse(sF1) = sF2,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF3 = multiply(sF0,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f25,plain,
multiply(sF0,sF2) = sF3,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF4 = multiply(sF2,sF0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f27,plain,
multiply(sF2,sF0) = sF4,
inference(reorient_equations,[],[f26]) ).
fof(f28,plain,
sF3 != sF4,
inference(definition_folding,[],[f17,f27,f19,f23,f21,f25,f23,f21,f19]) ).
fof(f29,plain,
sF0 = least_upper_bound(identity,a),
inference(forward_demodulation,[],[f19,f6]) ).
fof(f30,plain,
sF1 = greatest_lower_bound(identity,a),
inference(forward_demodulation,[],[f21,f5]) ).
fof(f82,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f3]) ).
fof(f83,plain,
! [X0] : multiply(sF0,multiply(sF2,X0)) = multiply(sF3,X0),
inference(superposition,[],[f4,f25]) ).
fof(f93,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f82,f1]) ).
fof(f104,plain,
! [X0] : multiply(sF2,multiply(sF1,X0)) = X0,
inference(superposition,[],[f93,f23]) ).
fof(f106,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[],[f93,f4]) ).
fof(f107,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f93,f3]) ).
fof(f108,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f93,f93]) ).
fof(f117,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f107,f108]) ).
fof(f125,plain,
! [X0,X1] : multiply(X0,greatest_lower_bound(identity,X1)) = greatest_lower_bound(X0,multiply(X0,X1)),
inference(superposition,[],[f14,f117]) ).
fof(f132,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f15,f1]) ).
fof(f163,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f16,f1]) ).
fof(f264,plain,
! [X0,X1] : multiply(X0,least_upper_bound(X1,multiply(X0,X1))) = multiply(least_upper_bound(identity,X0),multiply(X0,X1)),
inference(superposition,[],[f13,f132]) ).
fof(f265,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X0),multiply(X0,X1)) = multiply(X0,multiply(least_upper_bound(identity,X0),X1)),
inference(forward_demodulation,[],[f264,f132]) ).
fof(f910,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(superposition,[],[f3,f108]) ).
fof(f926,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[],[f117,f108]) ).
fof(f927,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f926,f117]) ).
fof(f949,plain,
sF1 = inverse(sF2),
inference(superposition,[],[f927,f23]) ).
fof(f1421,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),multiply(X0,identity)),
inference(superposition,[],[f106,f910]) ).
fof(f1488,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),X0),
inference(forward_demodulation,[],[f1421,f117]) ).
fof(f2070,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(inverse(X0)),inverse(multiply(X1,X0))),
inference(superposition,[],[f1488,f1488]) ).
fof(f2124,plain,
! [X0,X1] : inverse(X1) = multiply(X0,inverse(multiply(X1,X0))),
inference(forward_demodulation,[],[f2070,f927]) ).
fof(f2214,plain,
! [X0] : inverse(multiply(X0,sF1)) = multiply(sF2,inverse(X0)),
inference(superposition,[],[f104,f2124]) ).
fof(f4994,plain,
! [X0] : multiply(sF0,multiply(a,X0)) = multiply(a,multiply(sF0,X0)),
inference(superposition,[],[f265,f29]) ).
fof(f5217,plain,
multiply(sF0,multiply(a,identity)) = multiply(a,sF0),
inference(superposition,[],[f4994,f117]) ).
fof(f5244,plain,
multiply(a,sF0) = multiply(sF0,a),
inference(forward_demodulation,[],[f5217,f117]) ).
fof(f5269,plain,
greatest_lower_bound(sF0,multiply(sF0,a)) = multiply(greatest_lower_bound(identity,a),sF0),
inference(superposition,[],[f163,f5244]) ).
fof(f5274,plain,
greatest_lower_bound(sF0,multiply(sF0,a)) = multiply(sF1,sF0),
inference(forward_demodulation,[],[f5269,f30]) ).
fof(f5281,plain,
multiply(sF0,greatest_lower_bound(identity,a)) = multiply(sF1,sF0),
inference(forward_demodulation,[],[f5274,f125]) ).
fof(f5283,plain,
multiply(sF0,sF1) = multiply(sF1,sF0),
inference(forward_demodulation,[],[f5281,f30]) ).
fof(f5304,plain,
inverse(sF1) = multiply(sF0,inverse(multiply(sF0,sF1))),
inference(superposition,[],[f2124,f5283]) ).
fof(f5305,plain,
inverse(sF1) = multiply(sF0,multiply(sF2,inverse(sF0))),
inference(forward_demodulation,[],[f5304,f2214]) ).
fof(f5320,plain,
inverse(sF1) = multiply(sF3,inverse(sF0)),
inference(forward_demodulation,[],[f5305,f83]) ).
fof(f5328,plain,
sF2 = multiply(sF3,inverse(sF0)),
inference(forward_demodulation,[],[f5320,f23]) ).
fof(f5418,plain,
multiply(inverse(sF2),sF3) = inverse(inverse(sF0)),
inference(superposition,[],[f1488,f5328]) ).
fof(f5421,plain,
sF0 = multiply(inverse(sF2),sF3),
inference(forward_demodulation,[],[f5418,f927]) ).
fof(f5431,plain,
sF0 = multiply(sF1,sF3),
inference(forward_demodulation,[],[f5421,f949]) ).
fof(f5437,plain,
sF3 = multiply(sF2,sF0),
inference(superposition,[],[f104,f5431]) ).
fof(f5468,plain,
sF3 = sF4,
inference(backward_demodulation,[],[f27,f5437]) ).
fof(f5474,plain,
$false,
inference(forward_subsumption_resolution,[],[f5468,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP184-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:35:52 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 10.65/2.38 % (4158025)Detected a unit-equality problem, will run specialized UEQ schedule.
% 10.65/2.38 % (4158034)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=661953430:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 10.65/2.38 % (4158036)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2759129073:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 10.65/2.38 % (4158032)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3113314713:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 10.65/2.38 % (4158031)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=719338246:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 10.65/2.38 % (4158030)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=719331037:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 10.65/2.38 % (4158035)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2488462587:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 10.65/2.38 % (4158033)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2950061079:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 10.65/2.38 % (4158034)Instruction limit reached!
% 10.65/2.38 % (4158034)------------------------------
% 10.65/2.38 % (4158034)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.38 % (4158034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.38 % (4158034)CaDiCaL version: 2.1.3
% 10.65/2.38 % (4158034)Termination reason: Instruction limit
% 10.65/2.38 % (4158034)Termination phase: Saturation
% 10.65/2.38 % (4158034)Time elapsed: 0.059 s
% 10.65/2.38 % (4158034)Peak memory usage: 89 MB
% 10.65/2.38 % (4158034)Instructions burned: 182 (million)
% 10.65/2.38 % (4158033)Instruction limit reached!
% 10.65/2.38 % (4158033)------------------------------
% 10.65/2.38 % (4158033)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.38 % (4158033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.38 % (4158033)CaDiCaL version: 2.1.3
% 10.65/2.38 % (4158033)Termination reason: Instruction limit
% 10.65/2.38 % (4158033)Termination phase: Saturation
% 10.65/2.38 % (4158033)Time elapsed: 0.079 s
% 10.65/2.38 % (4158033)Peak memory usage: 89 MB
% 10.65/2.38 % (4158033)Instructions burned: 136 (million)
% 10.65/2.38 % (4158044)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2529503814:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 10.65/2.38 % (4158035)Instruction limit reached!
% 10.65/2.38 % (4158035)------------------------------
% 10.65/2.38 % (4158035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.38 % (4158035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.38 % (4158035)CaDiCaL version: 2.1.3
% 10.65/2.38 % (4158035)Termination reason: Instruction limit
% 10.65/2.38 % (4158035)Termination phase: Saturation
% 10.65/2.38 % (4158035)Time elapsed: 0.167 s
% 10.65/2.38 % (4158035)Peak memory usage: 91 MB
% 10.65/2.38 % (4158035)Instructions burned: 257 (million)
% 10.65/2.38 % (4158045)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=113822611:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 10.65/2.38 % (4158047)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1695401010:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 10.65/2.38 % (4158047)Instruction limit reached!
% 10.65/2.38 % (4158047)------------------------------
% 10.65/2.38 % (4158047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.38 % (4158047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.38 % (4158047)CaDiCaL version: 2.1.3
% 10.65/2.38 % (4158047)Termination reason: Instruction limit
% 10.65/2.38 % (4158047)Termination phase: Saturation
% 10.65/2.38 % (4158047)Time elapsed: 0.108 s
% 11.36/2.57 % (4158047)Peak memory usage: 90 MB
% 11.36/2.57 % (4158047)Instructions burned: 215 (million)
% 11.36/2.57 % (4158050)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=3677879013:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 11.36/2.57 % (4158036)Instruction limit reached!
% 11.36/2.57 % (4158036)------------------------------
% 11.36/2.57 % (4158036)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.36/2.57 % (4158036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.36/2.57 % (4158036)CaDiCaL version: 2.1.3
% 11.36/2.57 % (4158036)Termination reason: Instruction limit
% 11.36/2.57 % (4158036)Termination phase: Saturation
% 11.36/2.57 % (4158036)Time elapsed: 0.639 s
% 11.36/2.57 % (4158036)Peak memory usage: 99 MB
% 11.36/2.57 % (4158036)Instructions burned: 1188 (million)
% 11.36/2.57 % (4158050)Instruction limit reached!
% 11.36/2.57 % (4158050)------------------------------
% 11.36/2.57 % (4158050)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.36/2.57 % (4158050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.36/2.57 % (4158050)CaDiCaL version: 2.1.3
% 11.36/2.57 % (4158050)Termination reason: Instruction limit
% 11.36/2.57 % (4158050)Termination phase: Saturation
% 11.36/2.57 % (4158050)Time elapsed: 0.198 s
% 11.36/2.57 % (4158050)Peak memory usage: 93 MB
% 11.36/2.57 % (4158050)Instructions burned: 318 (million)
% 11.36/2.57 % (4158052)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=3846841718:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/12125Mi)
% 11.36/2.57 % (4158044)Instruction limit reached!
% 11.36/2.57 % (4158044)------------------------------
% 11.36/2.57 % (4158044)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.36/2.57 % (4158044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.36/2.57 % (4158044)CaDiCaL version: 2.1.3
% 11.36/2.57 % (4158044)Termination reason: Instruction limit
% 11.36/2.57 % (4158044)Termination phase: Saturation
% 11.36/2.57 % (4158044)Time elapsed: 0.726 s
% 11.36/2.57 % (4158044)Peak memory usage: 142 MB
% 11.36/2.57 % (4158044)Instructions burned: 2052 (million)
% 11.36/2.57 % (4158053)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=4055839736:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 11.36/2.57 % (4158055)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=1120301088:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2990 on theBenchmark for (2990ds/14534Mi)
% 11.36/2.57 % (4158032)First to succeed.
% 11.36/2.57 % (4158032)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4158025"
% 11.36/2.57 % (4158032)Refutation found. Thanks to Tanya!
% 11.36/2.57 % SZS status Unsatisfiable for theBenchmark
% 11.36/2.57 % SZS output start Proof for theBenchmark
% See solution above
% 11.36/2.57 % (4158032)------------------------------
% 11.36/2.57 % (4158032)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.36/2.57 % (4158032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.36/2.57 % (4158032)CaDiCaL version: 2.1.3
% 11.36/2.57 % (4158032)Termination reason: Refutation
% 11.36/2.57 % (4158032)Time elapsed: 1.129 s
% 11.36/2.57 % (4158032)Peak memory usage: 136 MB
% 11.36/2.57 % (4158032)Instructions burned: 1761 (million)
% 11.36/2.57 % (4158032)------------------------------
% 11.36/2.57 % (4158032)------------------------------
% 11.36/2.57 % (4158025)Success in time 1.525 s
% 11.36/2.57 % Vampire exiting
%------------------------------------------------------------------------------