%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO008-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 09:35:50 AM UTC 2026
% Result : Unsatisfiable 5.64s 1.58s
% Output : Refutation 5.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 44 unt; 0 def)
% Number of atoms : 44 ( 43 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 86 ( 86 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
fof(f3,axiom,
! [X2,X0,X1] : add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f4,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f5,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
fof(f6,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f10,axiom,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse1) ).
fof(f14,axiom,
! [X0] : multiply(multiplicative_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id2) ).
fof(f15,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id1) ).
fof(f16,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id2) ).
fof(f17,negated_conjecture,
add(a,add(b,c)) != add(add(a,b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity) ).
fof(f20,plain,
add(a,add(b,c)) != add(c,add(a,b)),
inference(forward_demodulation,[],[f17,f1]) ).
fof(f56,plain,
! [X0,X1] : multiply(X0,add(X1,inverse(X0))) = add(multiply(X0,X1),additive_identity),
inference(superposition,[],[f6,f10]) ).
fof(f67,plain,
! [X0,X1] : add(additive_identity,multiply(X0,X1)) = multiply(X0,add(X1,inverse(X0))),
inference(forward_demodulation,[],[f56,f1]) ).
fof(f70,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,add(X1,inverse(X0))),
inference(forward_demodulation,[],[f67,f16]) ).
fof(f74,plain,
! [X0,X1] : multiply(add(X0,X1),inverse(X0)) = add(additive_identity,multiply(X1,inverse(X0))),
inference(superposition,[],[f5,f10]) ).
fof(f95,plain,
! [X0,X1] : multiply(add(X0,X1),inverse(X0)) = multiply(X1,inverse(X0)),
inference(forward_demodulation,[],[f74,f16]) ).
fof(f97,plain,
! [X0,X1] : multiply(X1,inverse(X0)) = multiply(inverse(X0),add(X0,X1)),
inference(forward_demodulation,[],[f95,f2]) ).
fof(f117,plain,
! [X0,X1] : add(X0,multiply(additive_identity,X1)) = multiply(X0,add(X0,X1)),
inference(superposition,[],[f4,f15]) ).
fof(f192,plain,
! [X0,X1] : add(multiply(X0,X1),inverse(X0)) = multiply(multiplicative_identity,add(X1,inverse(X0))),
inference(superposition,[],[f3,f7]) ).
fof(f224,plain,
! [X0,X1] : add(X1,inverse(X0)) = add(multiply(X0,X1),inverse(X0)),
inference(forward_demodulation,[],[f192,f14]) ).
fof(f228,plain,
! [X0,X1] : add(X1,inverse(X0)) = add(inverse(X0),multiply(X0,X1)),
inference(forward_demodulation,[],[f224,f1]) ).
fof(f233,plain,
! [X0] : multiply(X0,inverse(X0)) = multiply(X0,additive_identity),
inference(superposition,[],[f70,f16]) ).
fof(f251,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(forward_demodulation,[],[f233,f10]) ).
fof(f293,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(superposition,[],[f2,f251]) ).
fof(f659,plain,
! [X0,X1] : add(add(X0,X1),inverse(X0)) = add(inverse(X0),add(X0,multiply(additive_identity,X1))),
inference(superposition,[],[f228,f117]) ).
fof(f694,plain,
! [X0,X1] : add(add(X0,X1),inverse(X0)) = add(inverse(X0),add(X0,additive_identity)),
inference(forward_demodulation,[],[f659,f293]) ).
fof(f706,plain,
! [X0,X1] : add(inverse(X0),X0) = add(add(X0,X1),inverse(X0)),
inference(forward_demodulation,[],[f694,f15]) ).
fof(f716,plain,
! [X0,X1] : add(inverse(X0),X0) = add(inverse(X0),add(X0,X1)),
inference(forward_demodulation,[],[f706,f1]) ).
fof(f718,plain,
! [X0,X1] : add(X0,inverse(X0)) = add(inverse(X0),add(X0,X1)),
inference(forward_demodulation,[],[f716,f1]) ).
fof(f719,plain,
! [X0,X1] : multiplicative_identity = add(inverse(X0),add(X0,X1)),
inference(forward_demodulation,[],[f718,f7]) ).
fof(f739,plain,
! [X2,X0,X1] : add(multiply(inverse(X0),X1),add(X0,X2)) = multiply(multiplicative_identity,add(X1,add(X0,X2))),
inference(superposition,[],[f3,f719]) ).
fof(f740,plain,
! [X2,X0,X1] : add(multiply(X0,inverse(X1)),add(X1,X2)) = multiply(add(X0,add(X1,X2)),multiplicative_identity),
inference(superposition,[],[f3,f719]) ).
fof(f754,plain,
! [X2,X0,X1] : add(multiply(X0,inverse(X1)),add(X1,X2)) = multiply(multiplicative_identity,add(X0,add(X1,X2))),
inference(forward_demodulation,[],[f740,f2]) ).
fof(f755,plain,
! [X2,X0,X1] : add(X1,add(X0,X2)) = add(multiply(inverse(X0),X1),add(X0,X2)),
inference(forward_demodulation,[],[f739,f14]) ).
fof(f764,plain,
! [X2,X0,X1] : add(multiply(X0,inverse(X1)),add(X1,X2)) = add(X0,add(X1,X2)),
inference(forward_demodulation,[],[f754,f14]) ).
fof(f768,plain,
! [X2,X0,X1] : add(multiply(X0,inverse(X1)),add(X1,X2)) = add(add(X1,X0),add(X1,X2)),
inference(superposition,[],[f755,f97]) ).
fof(f831,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X1,X0),add(X1,X2)),
inference(forward_demodulation,[],[f768,f764]) ).
fof(f962,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X1,X2),add(X1,X0)),
inference(superposition,[],[f1,f831]) ).
fof(f1263,plain,
! [X2,X0,X1] : add(X2,add(X1,X0)) = add(X0,add(X1,X2)),
inference(superposition,[],[f831,f962]) ).
fof(f1394,plain,
! [X2,X0,X1] : add(X2,add(X0,X1)) = add(X0,add(X1,X2)),
inference(superposition,[],[f1263,f1]) ).
fof(f1758,plain,
add(a,add(b,c)) != add(a,add(b,c)),
inference(superposition,[],[f20,f1394]) ).
fof(f1800,plain,
$false,
inference(trivial_inequality_removal,[],[f1758]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO008-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n014.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 21:03:31 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running first-order theorem proving
% 0.10/0.23 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
% 5.64/1.58 % (2185162)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.64/1.58 % (2185168)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=101646319:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.64/1.58 % (2185171)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2617975700:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.64/1.58 % (2185173)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=73667902:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.64/1.58 % (2185169)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2547659976:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.64/1.58 % (2185170)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3162115574:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.64/1.58 % (2185172)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2698509727:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.64/1.58 % (2185167)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=826366948:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.64/1.58 % (2185170)Instruction limit reached!
% 5.64/1.58 % (2185170)------------------------------
% 5.64/1.58 % (2185170)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.58 % (2185170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.58 % (2185170)CaDiCaL version: 2.1.3
% 5.64/1.58 % (2185170)Termination reason: Instruction limit
% 5.64/1.58 % (2185170)Termination phase: Saturation
% 5.64/1.58 % (2185170)Time elapsed: 0.082 s
% 5.64/1.58 % (2185170)Peak memory usage: 88 MB
% 5.64/1.58 % (2185170)Instructions burned: 138 (million)
% 5.64/1.58 % (2185171)Instruction limit reached!
% 5.64/1.58 % (2185171)------------------------------
% 5.64/1.58 % (2185171)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.58 % (2185171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.58 % (2185171)CaDiCaL version: 2.1.3
% 5.64/1.58 % (2185171)Termination reason: Instruction limit
% 5.64/1.58 % (2185171)Termination phase: Saturation
% 5.64/1.58 % (2185171)Time elapsed: 0.103 s
% 5.64/1.58 % (2185171)Peak memory usage: 89 MB
% 5.64/1.58 % (2185171)Instructions burned: 181 (million)
% 5.64/1.58 % (2185172)Instruction limit reached!
% 5.64/1.58 % (2185172)------------------------------
% 5.64/1.58 % (2185172)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.58 % (2185172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.58 % (2185172)CaDiCaL version: 2.1.3
% 5.64/1.58 % (2185172)Termination reason: Instruction limit
% 5.64/1.58 % (2185172)Termination phase: Saturation
% 5.64/1.58 % (2185172)Time elapsed: 0.167 s
% 5.64/1.58 % (2185172)Peak memory usage: 89 MB
% 5.64/1.58 % (2185172)Instructions burned: 257 (million)
% 5.64/1.58 % (2185181)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3995390013:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 5.64/1.58 % (2185182)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1066419505:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 5.64/1.58 % (2185183)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=397594316:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 5.64/1.58 % (2185168)First to succeed.
% 5.64/1.58 % (2185168)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2185162"
% 5.64/1.58 % (2185183)Instruction limit reached!
% 5.64/1.58 % (2185183)------------------------------
% 5.64/1.58 % (2185183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.58 % (2185183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.58 % (2185183)CaDiCaL version: 2.1.3
% 5.64/1.58 % (2185183)Termination reason: Instruction limit
% 5.64/1.58 % (2185183)Termination phase: Saturation
% 5.64/1.58 % (2185183)Time elapsed: 0.105 s
% 5.64/1.58 % (2185183)Peak memory usage: 89 MB
% 5.64/1.58 % (2185183)Instructions burned: 215 (million)
% 5.64/1.58 % (2185168)Refutation found. Thanks to Tanya!
% 5.64/1.58 % SZS status Unsatisfiable for theBenchmark
% 5.64/1.58 % SZS output start Proof for theBenchmark
% See solution above
% 5.64/1.58 % (2185168)------------------------------
% 5.64/1.58 % (2185168)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.58 % (2185168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.58 % (2185168)CaDiCaL version: 2.1.3
% 5.64/1.58 % (2185168)Termination reason: Refutation
% 5.64/1.58 % (2185168)Time elapsed: 0.416 s
% 5.64/1.58 % (2185168)Peak memory usage: 130 MB
% 5.64/1.58 % (2185168)Instructions burned: 1104 (million)
% 5.64/1.58 % (2185168)------------------------------
% 5.64/1.58 % (2185168)------------------------------
% 5.64/1.58 % (2185162)Success in time 0.71 s
% 5.64/1.58 % Vampire exiting
%------------------------------------------------------------------------------