%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP170-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 9.22s 2.28s
% Output : Refutation 9.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 25 ( 25 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
fof(f8,axiom,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_lub) ).
fof(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
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/sandbox/benchmark/theBenchmark.p',monotony_lub1) ).
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/sandbox/benchmark/theBenchmark.p',monotony_lub2) ).
fof(f17,axiom,
least_upper_bound(a,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p03d_1) ).
fof(f18,plain,
b = least_upper_bound(a,b),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
greatest_lower_bound(c,d) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p03d_2) ).
fof(f20,plain,
c = greatest_lower_bound(c,d),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p03d) ).
fof(f22,plain,
multiply(b,d) != least_upper_bound(multiply(a,c),multiply(b,d)),
inference(reorient_equations,[],[f21]) ).
fof(f23,plain,
multiply(b,d) != least_upper_bound(multiply(b,d),multiply(a,c)),
inference(forward_demodulation,[],[f22,f6]) ).
fof(f24,plain,
b = least_upper_bound(b,a),
inference(forward_demodulation,[],[f18,f6]) ).
fof(f46,plain,
! [X0,X1] : least_upper_bound(X1,greatest_lower_bound(X0,X1)) = X1,
inference(superposition,[],[f11,f5]) ).
fof(f47,plain,
d = least_upper_bound(d,c),
inference(superposition,[],[f46,f20]) ).
fof(f50,plain,
d = least_upper_bound(c,d),
inference(forward_demodulation,[],[f47,f6]) ).
fof(f89,plain,
! [X2,X3,X0,X1] : least_upper_bound(multiply(X0,X1),least_upper_bound(multiply(X0,X2),X3)) = least_upper_bound(multiply(X0,least_upper_bound(X1,X2)),X3),
inference(superposition,[],[f8,f13]) ).
fof(f109,plain,
! [X2,X3,X0,X1] : least_upper_bound(multiply(X0,least_upper_bound(X3,X2)),multiply(X1,X2)) = least_upper_bound(multiply(X0,X3),multiply(least_upper_bound(X0,X1),X2)),
inference(superposition,[],[f89,f15]) ).
fof(f153,plain,
! [X0,X1] : least_upper_bound(multiply(X0,c),multiply(least_upper_bound(X0,X1),d)) = least_upper_bound(multiply(X0,d),multiply(X1,d)),
inference(superposition,[],[f109,f50]) ).
fof(f208,plain,
! [X0,X1] : multiply(least_upper_bound(X0,X1),d) = least_upper_bound(multiply(X0,c),multiply(least_upper_bound(X0,X1),d)),
inference(forward_demodulation,[],[f153,f15]) ).
fof(f288,plain,
! [X0,X1] : multiply(least_upper_bound(X0,X1),d) = least_upper_bound(multiply(X1,c),multiply(least_upper_bound(X0,X1),d)),
inference(superposition,[],[f208,f6]) ).
fof(f502,plain,
multiply(b,d) = least_upper_bound(multiply(a,c),multiply(b,d)),
inference(superposition,[],[f288,f24]) ).
fof(f521,plain,
multiply(b,d) = least_upper_bound(multiply(b,d),multiply(a,c)),
inference(forward_demodulation,[],[f502,f6]) ).
fof(f540,plain,
$false,
inference(forward_subsumption_resolution,[],[f521,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP170-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:40:16 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.22/2.28 % (2368673)Detected a unit-equality problem, will run specialized UEQ schedule.
% 9.22/2.28 % (2368779)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=1804212423:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 9.22/2.28 % (2368785)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1265766834:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 9.22/2.28 % (2368780)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=1971623996:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 9.22/2.28 % (2368781)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1020448503:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 9.22/2.28 % (2368783)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2512172973:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 9.22/2.28 % (2368784)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2349623075:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 9.22/2.28 % (2368782)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2543313570:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 9.22/2.28 % (2368783)Instruction limit reached!
% 9.22/2.28 % (2368783)------------------------------
% 9.22/2.28 % (2368783)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.22/2.28 % (2368783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.22/2.28 % (2368783)CaDiCaL version: 2.1.3
% 9.22/2.28 % (2368783)Termination reason: Instruction limit
% 9.22/2.28 % (2368783)Termination phase: Saturation
% 9.22/2.28 % (2368783)Time elapsed: 0.107 s
% 9.22/2.28 % (2368783)Peak memory usage: 89 MB
% 9.22/2.28 % (2368783)Instructions burned: 181 (million)
% 9.22/2.28 % (2368782)Instruction limit reached!
% 9.22/2.28 % (2368782)------------------------------
% 9.22/2.28 % (2368782)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.22/2.28 % (2368782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.22/2.28 % (2368782)CaDiCaL version: 2.1.3
% 9.22/2.28 % (2368782)Termination reason: Instruction limit
% 9.22/2.28 % (2368782)Termination phase: Saturation
% 9.22/2.28 % (2368782)Time elapsed: 0.082 s
% 9.22/2.28 % (2368782)Peak memory usage: 89 MB
% 9.22/2.28 % (2368782)Instructions burned: 137 (million)
% 9.22/2.28 % (2368784)Instruction limit reached!
% 9.22/2.28 % (2368784)------------------------------
% 9.22/2.28 % (2368784)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.22/2.28 % (2368784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.22/2.28 % (2368784)CaDiCaL version: 2.1.3
% 9.22/2.28 % (2368784)Termination reason: Instruction limit
% 9.22/2.28 % (2368784)Termination phase: Saturation
% 9.22/2.28 % (2368784)Time elapsed: 0.167 s
% 9.22/2.28 % (2368784)Peak memory usage: 91 MB
% 9.22/2.28 % (2368784)Instructions burned: 258 (million)
% 9.22/2.28 % (2368806)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=4187515620:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 9.22/2.28 % (2368807)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=413775494:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 9.22/2.28 % (2368808)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3640695990:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 9.22/2.28 % (2368808)Instruction limit reached!
% 9.22/2.28 % (2368808)------------------------------
% 9.22/2.28 % (2368808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.22/2.28 % (2368808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.22/2.28 % (2368808)CaDiCaL version: 2.1.3
% 9.22/2.28 % (2368808)Termination reason: Instruction limit
% 9.22/2.28 % (2368808)Termination phase: Saturation
% 9.22/2.28 % (2368808)Time elapsed: 0.118 s
% 9.22/2.28 % (2368808)Peak memory usage: 93 MB
% 9.22/2.28 % (2368808)Instructions burned: 216 (million)
% 9.22/2.28 % (2368812)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=1133271677:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2993 on theBenchmark for (2993ds/317Mi)
% 9.22/2.28 % (2368780)First to succeed.
% 9.22/2.28 % (2368780)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2368673"
% 9.22/2.28 % (2368785)Instruction limit reached!
% 9.22/2.28 % (2368785)------------------------------
% 9.22/2.28 % (2368785)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.22/2.28 % (2368785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.22/2.28 % (2368785)CaDiCaL version: 2.1.3
% 9.22/2.28 % (2368785)Termination reason: Instruction limit
% 9.22/2.28 % (2368785)Termination phase: Saturation
% 9.22/2.28 % (2368785)Time elapsed: 0.783 s
% 9.22/2.28 % (2368785)Peak memory usage: 98 MB
% 9.22/2.28 % (2368785)Instructions burned: 1188 (million)
% 9.22/2.28 % (2368812)Instruction limit reached!
% 9.22/2.28 % (2368812)------------------------------
% 9.22/2.28 % (2368812)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.22/2.28 % (2368812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.22/2.28 % (2368812)CaDiCaL version: 2.1.3
% 9.22/2.28 % (2368812)Termination reason: Instruction limit
% 9.22/2.28 % (2368812)Termination phase: Saturation
% 9.22/2.28 % (2368812)Time elapsed: 0.242 s
% 9.22/2.28 % (2368812)Peak memory usage: 90 MB
% 9.22/2.28 % (2368812)Instructions burned: 317 (million)
% 9.22/2.28 % (2368824)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=3325834481:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2990 on theBenchmark for (2990ds/12125Mi)
% 9.22/2.28 % (2368780)Refutation found. Thanks to Tanya!
% 9.22/2.28 % SZS status Unsatisfiable for theBenchmark
% 9.22/2.28 % SZS output start Proof for theBenchmark
% See solution above
% 9.22/2.28 % (2368780)------------------------------
% 9.22/2.28 % (2368780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.22/2.28 % (2368780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.22/2.28 % (2368780)CaDiCaL version: 2.1.3
% 9.22/2.28 % (2368780)Termination reason: Refutation
% 9.22/2.28 % (2368780)Time elapsed: 0.700 s
% 9.22/2.28 % (2368780)Peak memory usage: 127 MB
% 9.22/2.28 % (2368780)Instructions burned: 1007 (million)
% 9.22/2.28 % (2368780)------------------------------
% 9.22/2.28 % (2368780)------------------------------
% 9.22/2.28 % (2368673)Success in time 1.224 s
% 9.22/2.28 % Vampire exiting
%------------------------------------------------------------------------------