%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP178-1 : 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 : 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 10:13:12 AM UTC 2026
% Result : Unsatisfiable 11.21s 3.15s
% Output : Refutation 11.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 47 ( 47 unt; 5 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 39 ( 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [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(f7,axiom,
! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).
fof(f12,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
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(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(f21,axiom,
least_upper_bound(identity,c) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p09a_3) ).
fof(f22,plain,
c = least_upper_bound(identity,c),
inference(reorient_equations,[],[f21]) ).
fof(f23,axiom,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p09a_4) ).
fof(f24,plain,
identity = greatest_lower_bound(a,b),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p09a) ).
fof(f32,definition,
sF2 = least_upper_bound(identity,c),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f33,plain,
least_upper_bound(identity,c) = sF2,
inference(reorient_equations,[],[f32]) ).
fof(f34,plain,
c = sF2,
inference(definition_folding,[],[f22,f33]) ).
fof(f35,definition,
sF3 = greatest_lower_bound(a,b),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f36,plain,
greatest_lower_bound(a,b) = sF3,
inference(reorient_equations,[],[f35]) ).
fof(f37,plain,
identity = sF3,
inference(definition_folding,[],[f24,f36]) ).
fof(f38,definition,
sF4 = multiply(b,c),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f39,plain,
multiply(b,c) = sF4,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF5 = greatest_lower_bound(a,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f41,plain,
greatest_lower_bound(a,sF4) = sF5,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF6 = greatest_lower_bound(a,c),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f43,plain,
greatest_lower_bound(a,c) = sF6,
inference(reorient_equations,[],[f42]) ).
fof(f44,plain,
sF5 != sF6,
inference(definition_folding,[],[f25,f43,f41,f39]) ).
fof(f47,plain,
c = least_upper_bound(identity,c),
inference(forward_demodulation,[],[f33,f34]) ).
fof(f48,plain,
identity = greatest_lower_bound(a,b),
inference(forward_demodulation,[],[f36,f37]) ).
fof(f49,plain,
sF5 = greatest_lower_bound(sF4,a),
inference(forward_demodulation,[],[f41,f5]) ).
fof(f52,plain,
identity = greatest_lower_bound(identity,c),
inference(superposition,[],[f12,f47]) ).
fof(f132,plain,
! [X2,X3,X0,X1] : greatest_lower_bound(multiply(X0,X1),greatest_lower_bound(multiply(X0,X2),X3)) = greatest_lower_bound(multiply(X0,greatest_lower_bound(X1,X2)),X3),
inference(superposition,[],[f7,f14]) ).
fof(f185,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f3]) ).
fof(f198,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f185,f1]) ).
fof(f211,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f198,f3]) ).
fof(f212,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f198,f198]) ).
fof(f226,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f211,f212]) ).
fof(f2301,plain,
! [X2,X3,X0,X1] : greatest_lower_bound(multiply(X0,greatest_lower_bound(X3,X2)),multiply(X1,X2)) = greatest_lower_bound(multiply(X0,X3),multiply(greatest_lower_bound(X0,X1),X2)),
inference(superposition,[],[f132,f16]) ).
fof(f3338,plain,
! [X0,X1] : greatest_lower_bound(multiply(X0,identity),multiply(greatest_lower_bound(X0,X1),c)) = greatest_lower_bound(multiply(X0,identity),multiply(X1,c)),
inference(superposition,[],[f2301,f52]) ).
fof(f3535,plain,
! [X0,X1] : greatest_lower_bound(X0,multiply(X1,c)) = greatest_lower_bound(X0,multiply(greatest_lower_bound(X0,X1),c)),
inference(forward_demodulation,[],[f3338,f226]) ).
fof(f3798,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,multiply(identity,c)),
inference(superposition,[],[f3535,f48]) ).
fof(f3877,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c),
inference(forward_demodulation,[],[f3798,f1]) ).
fof(f3918,plain,
greatest_lower_bound(a,multiply(b,c)) = sF6,
inference(forward_demodulation,[],[f3877,f43]) ).
fof(f3948,plain,
greatest_lower_bound(a,sF4) = sF6,
inference(forward_demodulation,[],[f3918,f39]) ).
fof(f3966,plain,
sF6 = greatest_lower_bound(sF4,a),
inference(forward_demodulation,[],[f3948,f5]) ).
fof(f3974,plain,
sF5 = sF6,
inference(forward_demodulation,[],[f3966,f49]) ).
fof(f3979,plain,
$false,
inference(forward_subsumption_resolution,[],[f3974,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP178-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.47 % Computer : n010.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.48 % CPULimit : 300
% 0.21/0.48 % WCLimit : 300
% 0.21/0.48 % DateTime : Sun Sep 27 09:36:01 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.54 Running first-order theorem proving
% 0.27/0.54 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
% 11.21/3.15 % (696817)Detected a unit-equality problem, will run specialized UEQ schedule.
% 11.21/3.15 % (696824)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2633372783:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 11.21/3.15 % (696823)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=2801448690:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 11.21/3.15 % (696822)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=1165525353:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 11.21/3.15 % (696825)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1891532683:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 11.21/3.15 % (696826)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=987080046:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 11.21/3.15 % (696826)Refutation not found, incomplete strategy
% 11.21/3.15 % (696826)------------------------------
% 11.21/3.15 % (696826)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.21/3.15 % (696826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.21/3.15 % (696826)CaDiCaL version: 2.1.3
% 11.21/3.15 % (696826)Termination reason: Refutation not found, incomplete strategy
% 11.21/3.15 % (696826)Time elapsed: 0.003 s
% 11.21/3.15 % (696826)Peak memory usage: 87 MB
% 11.21/3.15 % (696826)Instructions burned: 1 (million)
% 11.21/3.15 % (696828)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1317339439:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 11.21/3.15 % (696827)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=740733980:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 11.21/3.15 % (696825)Instruction limit reached!
% 11.21/3.15 % (696825)------------------------------
% 11.21/3.15 % (696825)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.21/3.15 % (696825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.21/3.15 % (696825)CaDiCaL version: 2.1.3
% 11.21/3.15 % (696825)Termination reason: Instruction limit
% 11.21/3.15 % (696825)Termination phase: Saturation
% 11.21/3.15 % (696825)Time elapsed: 0.141 s
% 11.21/3.15 % (696825)Peak memory usage: 89 MB
% 11.21/3.15 % (696825)Instructions burned: 136 (million)
% 11.21/3.15 % (696827)Instruction limit reached!
% 11.21/3.15 % (696827)------------------------------
% 11.21/3.15 % (696827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.21/3.15 % (696827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.21/3.15 % (696827)CaDiCaL version: 2.1.3
% 11.21/3.15 % (696827)Termination reason: Instruction limit
% 11.21/3.15 % (696827)Termination phase: Saturation
% 11.21/3.15 % (696827)Time elapsed: 0.272 s
% 11.21/3.15 % (696827)Peak memory usage: 91 MB
% 11.21/3.15 % (696827)Instructions burned: 257 (million)
% 11.21/3.15 % (696826)------------------------------
% 11.21/3.15 % (696826)------------------------------
% 11.21/3.15 % (696836)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3182934718:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 11.21/3.15 % (696838)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2100062824:i=4948:ss=axioms:sgt=16_2994 on theBenchmark for (2994ds/4948Mi)
% 11.21/3.15 % (696839)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2276566965:i=215:ep=RSTC_2992 on theBenchmark for (2992ds/215Mi)
% 11.21/3.15 % (696824)First to succeed.
% 11.21/3.15 % (696824)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-696817"
% 11.21/3.15 % (696839)Instruction limit reached!
% 11.21/3.15 % (696839)------------------------------
% 11.21/3.15 % (696839)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.21/3.15 % (696839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.21/3.15 % (696839)CaDiCaL version: 2.1.3
% 11.21/3.15 % (696839)Termination reason: Instruction limit
% 11.21/3.15 % (696839)Termination phase: Saturation
% 11.21/3.15 % (696839)Time elapsed: 0.203 s
% 11.21/3.15 % (696839)Peak memory usage: 93 MB
% 11.21/3.15 % (696839)Instructions burned: 215 (million)
% 11.21/3.15 % (696828)Instruction limit reached!
% 11.21/3.15 % (696828)------------------------------
% 11.21/3.15 % (696828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.21/3.15 % (696828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.21/3.15 % (696828)CaDiCaL version: 2.1.3
% 11.21/3.15 % (696828)Termination reason: Instruction limit
% 11.21/3.15 % (696828)Termination phase: Saturation
% 11.21/3.15 % (696828)Time elapsed: 1.094 s
% 11.21/3.15 % (696828)Peak memory usage: 99 MB
% 11.21/3.15 % (696828)Instructions burned: 1187 (million)
% 11.21/3.15 % (696824)Refutation found. Thanks to Tanya!
% 11.21/3.15 % SZS status Unsatisfiable for theBenchmark
% 11.21/3.15 % SZS output start Proof for theBenchmark
% See solution above
% 11.21/3.15 % (696824)------------------------------
% 11.21/3.15 % (696824)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.21/3.15 % (696824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.21/3.15 % (696824)CaDiCaL version: 2.1.3
% 11.21/3.15 % (696824)Termination reason: Refutation
% 11.21/3.15 % (696824)Time elapsed: 0.948 s
% 11.21/3.15 % (696824)Peak memory usage: 136 MB
% 11.21/3.15 % (696824)Instructions burned: 1582 (million)
% 11.21/3.15 % (696824)------------------------------
% 11.21/3.15 % (696824)------------------------------
% 11.21/3.15 % (696817)Success in time 1.428 s
% 11.21/3.15 % Vampire exiting
%------------------------------------------------------------------------------