%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP170-3 : 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 : n008.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 10:13:10 AM UTC 2026
% Result : Unsatisfiable 0.19s 2.04s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 21 ( 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f17,axiom,
least_upper_bound(a,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p03c_1) ).
fof(f18,plain,
b = least_upper_bound(a,b),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
least_upper_bound(c,d) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p03c_2) ).
fof(f20,plain,
d = least_upper_bound(c,d),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p03c) ).
fof(f22,plain,
multiply(a,c) != greatest_lower_bound(multiply(a,c),multiply(b,d)),
inference(reorient_equations,[],[f21]) ).
fof(f35,plain,
c = greatest_lower_bound(c,d),
inference(superposition,[],[f12,f20]) ).
fof(f36,plain,
a = greatest_lower_bound(a,b),
inference(superposition,[],[f12,f18]) ).
fof(f75,plain,
! [X2,X3,X0,X1] : greatest_lower_bound(multiply(X1,X2),greatest_lower_bound(multiply(X1,X0),X3)) = greatest_lower_bound(multiply(X1,greatest_lower_bound(X2,X0)),X3),
inference(superposition,[],[f7,f14]) ).
fof(f94,plain,
! [X2,X3,X0,X1] : greatest_lower_bound(multiply(X1,greatest_lower_bound(X3,X0)),multiply(X2,X0)) = greatest_lower_bound(multiply(X1,X3),multiply(greatest_lower_bound(X1,X2),X0)),
inference(superposition,[],[f75,f16]) ).
fof(f131,plain,
! [X0,X1] : greatest_lower_bound(multiply(X1,c),multiply(greatest_lower_bound(X1,X0),d)) = greatest_lower_bound(multiply(X1,c),multiply(X0,d)),
inference(superposition,[],[f94,f35]) ).
fof(f467,plain,
greatest_lower_bound(multiply(a,c),multiply(b,d)) = greatest_lower_bound(multiply(a,c),multiply(a,d)),
inference(superposition,[],[f131,f36]) ).
fof(f479,plain,
greatest_lower_bound(multiply(a,c),multiply(b,d)) = multiply(a,greatest_lower_bound(c,d)),
inference(forward_demodulation,[],[f467,f14]) ).
fof(f488,plain,
multiply(a,c) = greatest_lower_bound(multiply(a,c),multiply(b,d)),
inference(forward_demodulation,[],[f479,f35]) ).
fof(f493,plain,
$false,
inference(forward_subsumption_resolution,[],[f488,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP170-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n008.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 09:35:55 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 0.19/2.04 % (975748)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.19/2.04 % (975871)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4231013911:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.19/2.04 % (975864)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=1582398518:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.19/2.04 % (975867)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2348692374:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.19/2.04 % (975872)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=587918583:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.19/2.04 % (975866)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=109256039:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.19/2.04 % (975869)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4183444347:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.19/2.04 % (975870)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2796127917:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.19/2.04 % (975871)Instruction limit reached!
% 0.19/2.04 % (975871)------------------------------
% 0.19/2.04 % (975871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/2.04 % (975871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/2.04 % (975871)CaDiCaL version: 2.1.3
% 0.19/2.04 % (975871)Termination reason: Instruction limit
% 0.19/2.04 % (975871)Termination phase: Saturation
% 0.19/2.04 % (975871)Time elapsed: 0.087 s
% 0.19/2.04 % (975871)Peak memory usage: 91 MB
% 0.19/2.04 % (975871)Instructions burned: 257 (million)
% 0.19/2.04 % (975869)Instruction limit reached!
% 0.19/2.04 % (975869)------------------------------
% 0.19/2.04 % (975869)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/2.04 % (975869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/2.04 % (975869)CaDiCaL version: 2.1.3
% 0.19/2.04 % (975869)Termination reason: Instruction limit
% 0.19/2.04 % (975869)Termination phase: Saturation
% 0.19/2.04 % (975869)Time elapsed: 0.086 s
% 0.19/2.04 % (975869)Peak memory usage: 89 MB
% 0.19/2.04 % (975869)Instructions burned: 137 (million)
% 0.19/2.04 % (975870)Instruction limit reached!
% 0.19/2.04 % (975870)------------------------------
% 0.19/2.04 % (975870)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/2.04 % (975870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/2.04 % (975870)CaDiCaL version: 2.1.3
% 0.19/2.04 % (975870)Termination reason: Instruction limit
% 0.19/2.04 % (975870)Termination phase: Saturation
% 0.19/2.04 % (975870)Time elapsed: 0.108 s
% 0.19/2.04 % (975870)Peak memory usage: 89 MB
% 0.19/2.04 % (975870)Instructions burned: 181 (million)
% 0.19/2.04 % (975919)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1950396092:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 0.19/2.04 % (975920)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1511758105:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 0.19/2.04 % (975921)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1505668552:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 0.19/2.04 % (975921)Instruction limit reached!
% 0.19/2.04 % (975921)------------------------------
% 0.19/2.04 % (975921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/2.04 % (975921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/2.04 % (975921)CaDiCaL version: 2.1.3
% 0.19/2.04 % (975921)Termination reason: Instruction limit
% 0.19/2.04 % (975921)Termination phase: Saturation
% 0.19/2.04 % (975921)Time elapsed: 0.118 s
% 0.19/2.04 % (975921)Peak memory usage: 92 MB
% 0.19/2.04 % (975921)Instructions burned: 217 (million)
% 0.19/2.04 % (975925)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=1889259883: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)
% 0.19/2.04 % (975919)First to succeed.
% 0.19/2.04 % (975919)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-975748"
% 0.19/2.04 % (975866)Also succeeded, but the first one will report.
% 0.19/2.04 % (975872)Instruction limit reached!
% 0.19/2.04 % (975872)------------------------------
% 0.19/2.04 % (975872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/2.04 % (975872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/2.04 % (975872)CaDiCaL version: 2.1.3
% 0.19/2.04 % (975872)Termination reason: Instruction limit
% 0.19/2.04 % (975872)Termination phase: Saturation
% 0.19/2.04 % (975872)Time elapsed: 0.644 s
% 0.19/2.04 % (975872)Peak memory usage: 99 MB
% 0.19/2.04 % (975872)Instructions burned: 1189 (million)
% 0.19/2.04 % (975925)Instruction limit reached!
% 0.19/2.04 % (975925)------------------------------
% 0.19/2.04 % (975925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/2.04 % (975925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/2.04 % (975925)CaDiCaL version: 2.1.3
% 0.19/2.04 % (975925)Termination reason: Instruction limit
% 0.19/2.04 % (975925)Termination phase: Saturation
% 0.19/2.04 % (975925)Time elapsed: 0.187 s
% 0.19/2.04 % (975925)Peak memory usage: 91 MB
% 0.19/2.04 % (975925)Instructions burned: 318 (million)
% 0.19/2.04 % (975927)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=2085452074:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/12125Mi)
% 0.19/2.04 % (975928)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=1541887775:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 0.19/2.04 % (975929)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=502333267:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2991 on theBenchmark for (2991ds/14534Mi)
% 0.19/2.04 % (975919)Refutation found. Thanks to Tanya!
% 0.19/2.04 % SZS status Unsatisfiable for theBenchmark
% 0.19/2.04 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/2.04 % (975919)------------------------------
% 0.19/2.04 % (975919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/2.04 % (975919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/2.04 % (975919)CaDiCaL version: 2.1.3
% 0.19/2.04 % (975919)Termination reason: Refutation
% 0.19/2.04 % (975919)Time elapsed: 0.441 s
% 0.19/2.04 % (975919)Peak memory usage: 129 MB
% 0.19/2.04 % (975919)Instructions burned: 1017 (million)
% 0.19/2.04 % (975919)------------------------------
% 0.19/2.04 % (975919)------------------------------
% 0.19/2.04 % (975748)Success in time 0.985 s
% 0.19/2.04 % Vampire exiting
%------------------------------------------------------------------------------