%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP768-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 10:16:10 AM UTC 2026
% Result : Unsatisfiable 9.76s 2.39s
% Output : Refutation 9.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 40 unt; 0 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 74 ( 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : product(X0,difference(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
fof(f4,axiom,
! [X0,X1] : difference(X0,product(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
fof(f5,axiom,
! [X0,X1] : quotient(product(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
fof(f6,axiom,
! [X0,X1] : product(quotient(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
fof(f7,axiom,
! [X2,X0,X1] : difference(X0,product(product(X0,X1),X2)) = quotient(product(X1,product(X2,X0)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
fof(f9,axiom,
! [X0] : i(X0) = difference(X0,one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
fof(f10,axiom,
! [X0] : j(X0) = quotient(one,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
fof(f11,axiom,
! [X0] : product(i(X0),X0) = product(X0,j(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
fof(f12,axiom,
! [X0] : eta(X0) = product(i(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
fof(f13,plain,
! [X0] : product(i(X0),X0) = eta(X0),
inference(reorient_equations,[],[f12]) ).
fof(f17,axiom,
! [X2,X0,X1] : product(eta(X0),product(X1,X2)) = product(product(eta(X0),X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).
fof(f20,axiom,
! [X0,X1] : t(X0,X1) = quotient(product(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos19) ).
fof(f21,negated_conjecture,
t(eta(x0),product(x1,x2)) != product(t(eta(x0),x1),t(eta(x0),x2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f22,plain,
! [X0] : eta(X0) = product(difference(X0,one),X0),
inference(definition_unfolding,[],[f13,f9]) ).
fof(f23,plain,
! [X0] : product(difference(X0,one),X0) = product(X0,quotient(one,X0)),
inference(definition_unfolding,[],[f11,f9,f10]) ).
fof(f27,plain,
! [X2,X0,X1] : product(product(difference(X0,one),X0),product(X1,X2)) = product(product(product(difference(X0,one),X0),X1),X2),
inference(definition_unfolding,[],[f17,f22,f22]) ).
fof(f30,plain,
quotient(product(product(difference(x0,one),x0),product(x1,x2)),product(difference(x0,one),x0)) != product(quotient(product(product(difference(x0,one),x0),x1),product(difference(x0,one),x0)),quotient(product(product(difference(x0,one),x0),x2),product(difference(x0,one),x0))),
inference(definition_unfolding,[],[f21,f20,f22,f20,f22,f20,f22]) ).
fof(f81,plain,
! [X2,X0,X1] : quotient(product(X2,X0),X1) = difference(X1,product(product(X1,X2),quotient(X0,X1))),
inference(superposition,[],[f7,f6]) ).
fof(f114,plain,
! [X2,X0,X1] : product(product(X2,X0),quotient(X1,X2)) = product(X2,quotient(product(X0,X1),X2)),
inference(superposition,[],[f3,f81]) ).
fof(f402,plain,
! [X2,X0,X1] : product(X0,X1) = quotient(product(X0,quotient(product(X1,X2),X0)),quotient(X2,X0)),
inference(superposition,[],[f5,f114]) ).
fof(f570,plain,
quotient(product(product(x0,quotient(one,x0)),product(x1,x2)),product(x0,quotient(one,x0))) != product(quotient(product(product(x0,quotient(one,x0)),x1),product(x0,quotient(one,x0))),quotient(product(product(x0,quotient(one,x0)),x2),product(x0,quotient(one,x0)))),
inference(superposition,[],[f30,f23]) ).
fof(f660,plain,
! [X2,X0,X1] : product(X1,quotient(X0,X2)) = quotient(product(X1,quotient(X0,X1)),quotient(X2,X1)),
inference(superposition,[],[f402,f6]) ).
fof(f733,plain,
! [X2,X0,X1] : product(X1,quotient(product(X0,X1),X2)) = quotient(product(X1,X0),quotient(X2,X1)),
inference(superposition,[],[f660,f5]) ).
fof(f929,plain,
! [X2,X0,X1] : quotient(product(X1,X2),X0) = product(X1,quotient(product(X2,X1),product(X0,X1))),
inference(superposition,[],[f733,f5]) ).
fof(f1203,plain,
! [X2,X0,X1] : difference(X0,quotient(product(X0,X1),X2)) = quotient(product(X1,X0),product(X2,X0)),
inference(superposition,[],[f4,f929]) ).
fof(f1316,plain,
! [X2,X0,X1] : product(X1,X0) = product(difference(X0,quotient(product(X0,X1),X2)),product(X2,X0)),
inference(superposition,[],[f6,f1203]) ).
fof(f2851,plain,
! [X2,X0,X1] : product(product(X0,quotient(one,X0)),product(X1,X2)) = product(product(product(X0,quotient(one,X0)),X1),X2),
inference(superposition,[],[f27,f23]) ).
fof(f2873,plain,
! [X2,X0,X1] : product(product(difference(X0,one),X0),quotient(product(X1,X2),product(difference(X0,one),X0))) = product(product(difference(X0,one),X0),product(X1,quotient(X2,product(difference(X0,one),X0)))),
inference(superposition,[],[f114,f27]) ).
fof(f2874,plain,
! [X2,X0,X1] : quotient(product(X1,X2),product(difference(X0,one),X0)) = difference(product(difference(X0,one),X0),product(product(difference(X0,one),X0),product(X1,quotient(X2,product(difference(X0,one),X0))))),
inference(superposition,[],[f81,f27]) ).
fof(f2965,plain,
! [X2,X0,X1] : quotient(product(X1,X2),product(difference(X0,one),X0)) = product(X1,quotient(X2,product(difference(X0,one),X0))),
inference(forward_demodulation,[],[f2874,f4]) ).
fof(f2966,plain,
! [X2,X0,X1] : product(product(X0,quotient(one,X0)),quotient(product(X1,X2),product(X0,quotient(one,X0)))) = product(product(X0,quotient(one,X0)),product(X1,quotient(X2,product(X0,quotient(one,X0))))),
inference(forward_demodulation,[],[f2873,f23]) ).
fof(f3015,plain,
! [X2,X0,X1] : quotient(product(X1,X2),product(X0,quotient(one,X0))) = product(X1,quotient(X2,product(X0,quotient(one,X0)))),
inference(forward_demodulation,[],[f2965,f23]) ).
fof(f5283,plain,
quotient(product(product(x0,quotient(one,x0)),product(x1,x2)),product(x0,quotient(one,x0))) != product(quotient(product(product(x0,quotient(one,x0)),x1),product(x0,quotient(one,x0))),product(product(x0,quotient(one,x0)),quotient(x2,product(x0,quotient(one,x0))))),
inference(superposition,[],[f570,f3015]) ).
fof(f5290,plain,
! [X2,X0,X1] : product(X1,X0) = product(difference(X0,product(X0,quotient(X1,product(X2,quotient(one,X2))))),product(product(X2,quotient(one,X2)),X0)),
inference(superposition,[],[f1316,f3015]) ).
fof(f5337,plain,
! [X2,X0,X1] : product(X1,X0) = product(quotient(X1,product(X2,quotient(one,X2))),product(product(X2,quotient(one,X2)),X0)),
inference(forward_demodulation,[],[f5290,f4]) ).
fof(f5344,plain,
quotient(product(product(x0,quotient(one,x0)),product(x1,x2)),product(x0,quotient(one,x0))) != product(product(product(x0,quotient(one,x0)),quotient(x1,product(x0,quotient(one,x0)))),product(product(x0,quotient(one,x0)),quotient(x2,product(x0,quotient(one,x0))))),
inference(forward_demodulation,[],[f5283,f3015]) ).
fof(f5396,plain,
quotient(product(product(x0,quotient(one,x0)),product(x1,x2)),product(x0,quotient(one,x0))) != product(product(x0,quotient(one,x0)),product(quotient(x1,product(x0,quotient(one,x0))),product(product(x0,quotient(one,x0)),quotient(x2,product(x0,quotient(one,x0)))))),
inference(forward_demodulation,[],[f5344,f2851]) ).
fof(f5431,plain,
quotient(product(product(x0,quotient(one,x0)),product(x1,x2)),product(x0,quotient(one,x0))) != product(product(x0,quotient(one,x0)),product(x1,quotient(x2,product(x0,quotient(one,x0))))),
inference(forward_demodulation,[],[f5396,f5337]) ).
fof(f5445,plain,
product(product(x0,quotient(one,x0)),product(x1,quotient(x2,product(x0,quotient(one,x0))))) != product(product(x0,quotient(one,x0)),quotient(product(x1,x2),product(x0,quotient(one,x0)))),
inference(forward_demodulation,[],[f5431,f3015]) ).
fof(f5452,plain,
$false,
inference(forward_subsumption_resolution,[],[f5445,f2966]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP768-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n026.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 27 10:45:26 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 8.99/2.16 % (2648526)Detected a unit-equality problem, will run specialized UEQ schedule.
% 8.99/2.16 % (2648631)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=3156152374:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 8.99/2.16 % (2648630)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=1536519376:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 8.99/2.16 % (2648633)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=828788812:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 8.99/2.16 % (2648632)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3395810520:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 8.99/2.16 % (2648634)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=437162431:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 8.99/2.16 % (2648636)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2616093551:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 8.99/2.16 % (2648635)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=485444393:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 8.99/2.16 % (2648633)Instruction limit reached!
% 8.99/2.16 % (2648633)------------------------------
% 8.99/2.16 % (2648633)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.99/2.16 % (2648633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.99/2.16 % (2648633)CaDiCaL version: 2.1.3
% 8.99/2.16 % (2648633)Termination reason: Instruction limit
% 8.99/2.16 % (2648633)Termination phase: Saturation
% 8.99/2.16 % (2648633)Time elapsed: 0.139 s
% 8.99/2.16 % (2648633)Peak memory usage: 88 MB
% 8.99/2.16 % (2648633)Instructions burned: 136 (million)
% 8.99/2.16 % (2648634)Instruction limit reached!
% 8.99/2.16 % (2648634)------------------------------
% 8.99/2.16 % (2648634)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.99/2.16 % (2648634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.99/2.16 % (2648634)CaDiCaL version: 2.1.3
% 8.99/2.16 % (2648634)Termination reason: Instruction limit
% 8.99/2.16 % (2648634)Termination phase: Saturation
% 8.99/2.16 % (2648634)Time elapsed: 0.178 s
% 8.99/2.16 % (2648634)Peak memory usage: 89 MB
% 8.99/2.16 % (2648634)Instructions burned: 181 (million)
% 8.99/2.16 % (2648635)Instruction limit reached!
% 8.99/2.16 % (2648635)------------------------------
% 8.99/2.16 % (2648635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.99/2.16 % (2648635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.99/2.16 % (2648635)CaDiCaL version: 2.1.3
% 8.99/2.16 % (2648635)Termination reason: Instruction limit
% 8.99/2.16 % (2648635)Termination phase: Saturation
% 8.99/2.16 % (2648635)Time elapsed: 0.273 s
% 8.99/2.16 % (2648635)Peak memory usage: 90 MB
% 8.99/2.16 % (2648635)Instructions burned: 258 (million)
% 8.99/2.16 % (2648679)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2325874703:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 8.99/2.16 % (2648680)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2012756494:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 8.99/2.16 % (2648684)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1025697907:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 8.99/2.16 % (2648684)Instruction limit reached!
% 8.99/2.16 % (2648684)------------------------------
% 8.99/2.16 % (2648684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.99/2.16 % (2648684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.99/2.16 % (2648684)CaDiCaL version: 2.1.3
% 8.99/2.16 % (2648684)Termination reason: Instruction limit
% 8.99/2.16 % (2648684)Termination phase: Saturation
% 8.99/2.16 % (2648684)Time elapsed: 0.186 s
% 9.76/2.39 % (2648684)Peak memory usage: 89 MB
% 9.76/2.39 % (2648684)Instructions burned: 215 (million)
% 9.76/2.39 % (2648631)First to succeed.
% 9.76/2.39 % (2648631)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2648526"
% 9.76/2.39 % (2648691)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=3892221165:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2991 on theBenchmark for (2991ds/317Mi)
% 9.76/2.39 % (2648631)Refutation found. Thanks to Tanya!
% 9.76/2.39 % SZS status Unsatisfiable for theBenchmark
% 9.76/2.39 % SZS output start Proof for theBenchmark
% See solution above
% 9.76/2.39 % (2648631)------------------------------
% 9.76/2.39 % (2648631)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.76/2.39 % (2648631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.76/2.39 % (2648631)CaDiCaL version: 2.1.3
% 9.76/2.39 % (2648631)Termination reason: Refutation
% 9.76/2.39 % (2648631)Time elapsed: 0.968 s
% 9.76/2.39 % (2648631)Peak memory usage: 137 MB
% 9.76/2.39 % (2648631)Instructions burned: 1692 (million)
% 9.76/2.39 % (2648631)------------------------------
% 9.76/2.39 % (2648631)------------------------------
% 9.76/2.39 % (2648526)Success in time 1.302 s
% 9.76/2.39 % Vampire exiting
%------------------------------------------------------------------------------