%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD044-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 09:49:10 AM UTC 2026
% Result : Unsatisfiable 5.62s 1.55s
% Output : Refutation 5.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 38 ( 29 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 38 ( 20 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X4,X5,X2)
| ~ sum(X0,X3,X4)
| ~ sum(X3,X5,X1)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_1) ).
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f4,axiom,
! [X0] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_multiplication) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X5,X6,X2)
| ~ sum(X3,X4,X5)
| sum(X0,X1,X2)
| ~ product(X3,X6,X0)
| ~ product(X4,X6,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_1) ).
fof(f12,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X4,X1,X6)
| ~ sum(X3,X4,X0)
| ~ product(X3,X1,X5)
| product(X0,X1,X2)
| ~ sum(X5,X6,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_2) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
fof(f15,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f20,axiom,
! [X0,X1] :
( product(X0,X1,multiply(X0,X1))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_multiplication) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,axiom,
defined(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_defined) ).
fof(f30,negated_conjecture,
product(a,b,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_4) ).
fof(f31,negated_conjecture,
~ product(additive_inverse(a),b,additive_inverse(u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_5) ).
fof(f36,plain,
sum(additive_inverse(u),u,additive_identity),
inference(unit_resulting_resolution,[],[f4,f29]) ).
fof(f37,plain,
sum(additive_inverse(a),a,additive_identity),
inference(unit_resulting_resolution,[],[f4,f27]) ).
fof(f39,plain,
defined(additive_inverse(u)),
inference(unit_resulting_resolution,[],[f15,f29]) ).
fof(f40,plain,
defined(additive_inverse(a)),
inference(unit_resulting_resolution,[],[f15,f27]) ).
fof(f78,plain,
sum(additive_identity,additive_inverse(u),additive_inverse(u)),
inference(unit_resulting_resolution,[],[f3,f39]) ).
fof(f79,plain,
sum(additive_identity,additive_inverse(a),additive_inverse(a)),
inference(unit_resulting_resolution,[],[f3,f40]) ).
fof(f80,plain,
sum(additive_identity,a,a),
inference(unit_resulting_resolution,[],[f3,f27]) ).
fof(f82,plain,
sum(additive_identity,u,u),
inference(unit_resulting_resolution,[],[f3,f29]) ).
fof(f114,plain,
sum(u,additive_inverse(u),additive_identity),
inference(unit_resulting_resolution,[],[f5,f36]) ).
fof(f117,plain,
sum(additive_inverse(a),additive_identity,additive_inverse(a)),
inference(unit_resulting_resolution,[],[f5,f79]) ).
fof(f120,plain,
sum(u,additive_identity,u),
inference(unit_resulting_resolution,[],[f5,f82]) ).
fof(f173,plain,
product(b,additive_inverse(a),multiply(b,additive_inverse(a))),
inference(unit_resulting_resolution,[],[f20,f40,f28]) ).
fof(f559,plain,
product(b,additive_identity,multiply(b,additive_identity)),
inference(unit_resulting_resolution,[],[f20,f28,f14]) ).
fof(f567,plain,
product(additive_identity,b,multiply(b,additive_identity)),
inference(unit_resulting_resolution,[],[f10,f559]) ).
fof(f581,plain,
sum(multiply(b,additive_identity),u,u),
inference(unit_resulting_resolution,[],[f11,f30,f30,f80,f567]) ).
fof(f594,plain,
sum(multiply(b,additive_identity),additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f1,f114,f114,f581]) ).
fof(f714,plain,
product(additive_inverse(a),b,multiply(b,additive_inverse(a))),
inference(unit_resulting_resolution,[],[f10,f173]) ).
fof(f733,plain,
sum(multiply(b,additive_inverse(a)),u,multiply(b,additive_identity)),
inference(unit_resulting_resolution,[],[f11,f30,f567,f37,f714]) ).
fof(f741,plain,
sum(multiply(b,additive_inverse(a)),u,additive_identity),
inference(unit_resulting_resolution,[],[f1,f120,f594,f733]) ).
fof(f758,plain,
sum(multiply(b,additive_inverse(a)),additive_identity,additive_inverse(u)),
inference(unit_resulting_resolution,[],[f1,f78,f114,f741]) ).
fof(f773,plain,
product(additive_identity,b,additive_identity),
inference(unit_resulting_resolution,[],[f12,f30,f37,f714,f741]) ).
fof(f826,plain,
~ sum(multiply(b,additive_inverse(a)),additive_identity,additive_inverse(u)),
inference(unit_resulting_resolution,[],[f12,f31,f714,f117,f773]) ).
fof(f828,plain,
$false,
inference(forward_subsumption_resolution,[],[f826,f758]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD044-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.16 % Computer : n014.cluster.edu
% 0.05/0.16 % Model : x86_64 x86_64
% 0.05/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.16 % Memory : 8046.5625MB
% 0.05/0.16 % OS : Linux 6.8.0-71-generic
% 0.05/0.16 % CPULimit : 300
% 0.05/0.16 % WCLimit : 300
% 0.05/0.16 % DateTime : Tue Sep 29 00:36:30 UTC 2026
% 0.05/0.17 % CPUTime :
% 0.05/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.20 Running first-order theorem proving
% 0.05/0.20 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
% 4.42/1.35 % (2334529)Input is clausal, will run a generic CNF schedule.
% 4.42/1.35 % (2334535)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=612149822:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.42/1.35 % (2334539)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3354744558:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.42/1.35 % (2334537)lrs+10_1_sil=8000:sp=occurrence:random_seed=602135836:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.42/1.35 % (2334534)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1193534871:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.42/1.35 % (2334536)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=105743643:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.42/1.35 % (2334538)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1821319081:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.42/1.35 % (2334540)dis-21_1_sil=8000:lcm=predicate:random_seed=1864278731:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 4.42/1.35 % (2334540)Instruction limit reached!
% 4.42/1.35 % (2334540)------------------------------
% 4.42/1.35 % (2334540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.42/1.35 % (2334540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.42/1.35 % (2334540)CaDiCaL version: 2.1.3
% 4.42/1.35 % (2334540)Termination reason: Instruction limit
% 4.42/1.35 % (2334540)Termination phase: Saturation
% 4.42/1.35 % (2334540)Time elapsed: 0.054 s
% 4.42/1.35 % (2334540)Peak memory usage: 88 MB
% 4.42/1.35 % (2334540)Instructions burned: 118 (million)
% 4.42/1.35 % (2334538)Instruction limit reached!
% 4.42/1.35 % (2334538)------------------------------
% 4.42/1.35 % (2334538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.42/1.35 % (2334538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.42/1.35 % (2334538)CaDiCaL version: 2.1.3
% 4.42/1.35 % (2334538)Termination reason: Instruction limit
% 4.42/1.35 % (2334538)Termination phase: Saturation
% 4.42/1.35 % (2334538)Time elapsed: 0.060 s
% 4.42/1.35 % (2334538)Peak memory usage: 88 MB
% 4.42/1.35 % (2334538)Instructions burned: 114 (million)
% 4.42/1.35 % (2334537)Instruction limit reached!
% 4.42/1.35 % (2334537)------------------------------
% 4.42/1.35 % (2334537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.42/1.35 % (2334537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.42/1.35 % (2334537)CaDiCaL version: 2.1.3
% 4.42/1.35 % (2334537)Termination reason: Instruction limit
% 4.42/1.35 % (2334537)Termination phase: Saturation
% 4.42/1.35 % (2334537)Time elapsed: 0.068 s
% 4.42/1.35 % (2334537)Peak memory usage: 88 MB
% 4.42/1.35 % (2334537)Instructions burned: 107 (million)
% 4.42/1.35 % (2334539)Instruction limit reached!
% 4.42/1.35 % (2334539)------------------------------
% 4.42/1.35 % (2334539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.42/1.35 % (2334539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.42/1.35 % (2334539)CaDiCaL version: 2.1.3
% 4.42/1.35 % (2334539)Termination reason: Instruction limit
% 4.42/1.35 % (2334539)Termination phase: Saturation
% 4.42/1.35 % (2334539)Time elapsed: 0.106 s
% 4.42/1.35 % (2334539)Peak memory usage: 89 MB
% 4.42/1.35 % (2334539)Instructions burned: 181 (million)
% 4.42/1.35 % (2334548)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1329353260:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.42/1.35 % (2334549)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=435658859:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 4.42/1.35 % (2334550)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2639711211:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.42/1.35 % (2334551)lrs+10_64_to=lpo:sil=8000:random_seed=4237314296:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 4.42/1.35 % (2334548)Instruction limit reached!
% 5.62/1.55 % (2334548)------------------------------
% 5.62/1.55 % (2334548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.62/1.55 % (2334548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.55 % (2334548)CaDiCaL version: 2.1.3
% 5.62/1.55 % (2334548)Termination reason: Instruction limit
% 5.62/1.55 % (2334548)Termination phase: Saturation
% 5.62/1.55 % (2334548)Time elapsed: 0.084 s
% 5.62/1.55 % (2334548)Peak memory usage: 89 MB
% 5.62/1.55 % (2334548)Instructions burned: 143 (million)
% 5.62/1.55 % (2334549)Instruction limit reached!
% 5.62/1.55 % (2334549)------------------------------
% 5.62/1.55 % (2334549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.62/1.55 % (2334549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.55 % (2334549)CaDiCaL version: 2.1.3
% 5.62/1.55 % (2334549)Termination reason: Instruction limit
% 5.62/1.55 % (2334549)Termination phase: Saturation
% 5.62/1.55 % (2334549)Time elapsed: 0.095 s
% 5.62/1.55 % (2334549)Peak memory usage: 93 MB
% 5.62/1.55 % (2334549)Instructions burned: 190 (million)
% 5.62/1.55 % (2334551)Instruction limit reached!
% 5.62/1.55 % (2334551)------------------------------
% 5.62/1.55 % (2334551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.62/1.55 % (2334551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.55 % (2334551)CaDiCaL version: 2.1.3
% 5.62/1.55 % (2334551)Termination reason: Instruction limit
% 5.62/1.55 % (2334551)Termination phase: Saturation
% 5.62/1.55 % (2334551)Time elapsed: 0.077 s
% 5.62/1.55 % (2334551)Peak memory usage: 89 MB
% 5.62/1.55 % (2334551)Instructions burned: 127 (million)
% 5.62/1.55 % (2334550)Instruction limit reached!
% 5.62/1.55 % (2334550)------------------------------
% 5.62/1.55 % (2334550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.62/1.55 % (2334550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.55 % (2334550)CaDiCaL version: 2.1.3
% 5.62/1.55 % (2334550)Termination reason: Instruction limit
% 5.62/1.55 % (2334550)Termination phase: Saturation
% 5.62/1.55 % (2334550)Time elapsed: 0.128 s
% 5.62/1.55 % (2334550)Peak memory usage: 89 MB
% 5.62/1.55 % (2334550)Instructions burned: 221 (million)
% 5.62/1.55 % (2334535)First to succeed.
% 5.62/1.55 % (2334535)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2334529"
% 5.62/1.55 % (2334556)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=910443555:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.62/1.55 % (2334557)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=860620125:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 5.62/1.55 % (2334558)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=4078223679:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 5.62/1.55 % (2334559)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=3564115763:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2994 on theBenchmark for (2994ds/106Mi)
% 5.62/1.55 % (2334535)Refutation found. Thanks to Tanya!
% 5.62/1.55 % SZS status Unsatisfiable for theBenchmark
% 5.62/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 5.62/1.55 % (2334535)------------------------------
% 5.62/1.55 % (2334535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.62/1.55 % (2334535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.55 % (2334535)CaDiCaL version: 2.1.3
% 5.62/1.55 % (2334535)Termination reason: Refutation
% 5.62/1.55 % (2334535)Time elapsed: 0.427 s
% 5.62/1.55 % (2334535)Peak memory usage: 129 MB
% 5.62/1.55 % (2334535)Instructions burned: 1059 (million)
% 5.62/1.55 % (2334535)------------------------------
% 5.62/1.55 % (2334535)------------------------------
% 5.62/1.55 % (2334529)Success in time 0.711 s
% 5.62/1.55 % Vampire exiting
%------------------------------------------------------------------------------