%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD066-3 : 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 : 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 09:49:19 AM UTC 2026
% Result : Unsatisfiable 5.25s 1.52s
% Output : Refutation 5.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of formulae : 23 ( 18 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 16 ( 16 !; 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(f24,axiom,
! [X2,X3,X0,X1,X4] :
( ~ sum(X3,X4,X1)
| ~ less_or_equal(X2,X3)
| ~ sum(X2,X4,X0)
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
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(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
fof(f32,negated_conjecture,
sum(a,c,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_6) ).
fof(f33,negated_conjecture,
sum(b,c,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_7) ).
fof(f34,negated_conjecture,
less_or_equal(u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_8) ).
fof(f35,negated_conjecture,
~ less_or_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_9) ).
fof(f36,plain,
sum(c,a,u),
inference(unit_resulting_resolution,[],[f5,f32]) ).
fof(f37,plain,
sum(c,b,v),
inference(unit_resulting_resolution,[],[f5,f33]) ).
fof(f50,plain,
sum(additive_identity,a,a),
inference(unit_resulting_resolution,[],[f3,f27]) ).
fof(f61,plain,
sum(additive_identity,b,b),
inference(unit_resulting_resolution,[],[f3,f28]) ).
fof(f94,plain,
sum(additive_inverse(c),c,additive_identity),
inference(unit_resulting_resolution,[],[f4,f29]) ).
fof(f98,plain,
sum(additive_inverse(c),u,a),
inference(unit_resulting_resolution,[],[f1,f50,f36,f94]) ).
fof(f99,plain,
sum(additive_inverse(c),v,b),
inference(unit_resulting_resolution,[],[f1,f61,f37,f94]) ).
fof(f105,plain,
sum(v,additive_inverse(c),b),
inference(unit_resulting_resolution,[],[f5,f99]) ).
fof(f111,plain,
~ sum(u,additive_inverse(c),a),
inference(unit_resulting_resolution,[],[f24,f35,f34,f105]) ).
fof(f117,plain,
sum(u,additive_inverse(c),a),
inference(unit_resulting_resolution,[],[f5,f98]) ).
fof(f118,plain,
$false,
inference(forward_subsumption_resolution,[],[f117,f111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD066-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n026.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 00:50:42 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 5.25/1.52 % (255060)Input is clausal, will run a generic CNF schedule.
% 5.25/1.52 % (255066)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3532567562:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.25/1.52 % (255067)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1951506075:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.25/1.52 % (255069)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2359519959:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.25/1.52 % (255065)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=2145163267:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.25/1.52 % (255068)lrs+10_1_sil=8000:sp=occurrence:random_seed=1327876297:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.25/1.52 % (255071)dis-21_1_sil=8000:lcm=predicate:random_seed=362358902: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)
% 5.25/1.52 % (255070)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=428510144:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.25/1.52 % (255069)Instruction limit reached!
% 5.25/1.52 % (255069)------------------------------
% 5.25/1.52 % (255069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.52 % (255069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.52 % (255069)CaDiCaL version: 2.1.3
% 5.25/1.52 % (255069)Termination reason: Instruction limit
% 5.25/1.52 % (255069)Termination phase: Saturation
% 5.25/1.52 % (255069)Time elapsed: 0.061 s
% 5.25/1.52 % (255069)Peak memory usage: 88 MB
% 5.25/1.52 % (255069)Instructions burned: 115 (million)
% 5.25/1.52 % (255068)Instruction limit reached!
% 5.25/1.52 % (255068)------------------------------
% 5.25/1.52 % (255068)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.52 % (255068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.52 % (255068)CaDiCaL version: 2.1.3
% 5.25/1.52 % (255068)Termination reason: Instruction limit
% 5.25/1.52 % (255068)Termination phase: Saturation
% 5.25/1.52 % (255068)Time elapsed: 0.069 s
% 5.25/1.52 % (255068)Peak memory usage: 88 MB
% 5.25/1.52 % (255068)Instructions burned: 109 (million)
% 5.25/1.52 % (255071)Instruction limit reached!
% 5.25/1.52 % (255071)------------------------------
% 5.25/1.52 % (255071)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.52 % (255071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.52 % (255071)CaDiCaL version: 2.1.3
% 5.25/1.52 % (255071)Termination reason: Instruction limit
% 5.25/1.52 % (255071)Termination phase: Saturation
% 5.25/1.52 % (255071)Time elapsed: 0.072 s
% 5.25/1.52 % (255071)Peak memory usage: 89 MB
% 5.25/1.52 % (255071)Instructions burned: 117 (million)
% 5.25/1.52 % (255070)Instruction limit reached!
% 5.25/1.52 % (255070)------------------------------
% 5.25/1.52 % (255070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.52 % (255070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.52 % (255070)CaDiCaL version: 2.1.3
% 5.25/1.52 % (255070)Termination reason: Instruction limit
% 5.25/1.52 % (255070)Termination phase: Saturation
% 5.25/1.52 % (255070)Time elapsed: 0.112 s
% 5.25/1.52 % (255070)Peak memory usage: 89 MB
% 5.25/1.52 % (255070)Instructions burned: 180 (million)
% 5.25/1.52 % (255080)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3693514461: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)
% 5.25/1.52 % (255079)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=387404774:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.25/1.52 % (255081)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3494638799:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.25/1.52 % (255082)lrs+10_64_to=lpo:sil=8000:random_seed=3464638833:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.25/1.52 % (255079)Instruction limit reached!
% 5.25/1.52 % (255079)------------------------------
% 5.25/1.52 % (255079)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.52 % (255079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.52 % (255079)CaDiCaL version: 2.1.3
% 5.25/1.52 % (255079)Termination reason: Instruction limit
% 5.25/1.52 % (255079)Termination phase: Saturation
% 5.25/1.52 % (255079)Time elapsed: 0.082 s
% 5.25/1.52 % (255079)Peak memory usage: 89 MB
% 5.25/1.52 % (255079)Instructions burned: 144 (million)
% 5.25/1.52 % (255080)Instruction limit reached!
% 5.25/1.52 % (255080)------------------------------
% 5.25/1.52 % (255080)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.52 % (255080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.52 % (255080)CaDiCaL version: 2.1.3
% 5.25/1.52 % (255080)Termination reason: Instruction limit
% 5.25/1.52 % (255080)Termination phase: Saturation
% 5.25/1.52 % (255080)Time elapsed: 0.094 s
% 5.25/1.52 % (255080)Peak memory usage: 93 MB
% 5.25/1.52 % (255080)Instructions burned: 191 (million)
% 5.25/1.52 % (255082)Instruction limit reached!
% 5.25/1.52 % (255082)------------------------------
% 5.25/1.52 % (255082)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.52 % (255082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.52 % (255082)CaDiCaL version: 2.1.3
% 5.25/1.52 % (255082)Termination reason: Instruction limit
% 5.25/1.52 % (255082)Termination phase: Saturation
% 5.25/1.52 % (255082)Time elapsed: 0.055 s
% 5.25/1.52 % (255082)Peak memory usage: 87 MB
% 5.25/1.52 % (255082)Instructions burned: 128 (million)
% 5.25/1.52 % (255066)First to succeed.
% 5.25/1.52 % (255066)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-255060"
% 5.25/1.52 % (255081)Instruction limit reached!
% 5.25/1.52 % (255081)------------------------------
% 5.25/1.52 % (255081)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.52 % (255081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.52 % (255081)CaDiCaL version: 2.1.3
% 5.25/1.52 % (255081)Termination reason: Instruction limit
% 5.25/1.52 % (255081)Termination phase: Saturation
% 5.25/1.52 % (255081)Time elapsed: 0.124 s
% 5.25/1.52 % (255081)Peak memory usage: 89 MB
% 5.25/1.52 % (255081)Instructions burned: 219 (million)
% 5.25/1.52 % (255087)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=208153826:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.25/1.52 % (255088)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3863835825:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 5.25/1.52 % (255089)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=2616906907:i=3394:sd=4:ss=included:sgt=64_2995 on theBenchmark for (2995ds/3394Mi)
% 5.25/1.52 % (255087)Instruction limit reached!
% 5.25/1.52 % (255087)------------------------------
% 5.25/1.52 % (255087)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.52 % (255087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.52 % (255087)CaDiCaL version: 2.1.3
% 5.25/1.52 % (255087)Termination reason: Instruction limit
% 5.25/1.52 % (255087)Termination phase: Saturation
% 5.25/1.52 % (255087)Time elapsed: 0.071 s
% 5.25/1.52 % (255087)Peak memory usage: 87 MB
% 5.25/1.52 % (255087)Instructions burned: 196 (million)
% 5.25/1.52 % (255090)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=3748636184:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2995 on theBenchmark for (2995ds/106Mi)
% 5.25/1.52 % (255066)Refutation found. Thanks to Tanya!
% 5.25/1.52 % SZS status Unsatisfiable for theBenchmark
% 5.25/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 5.25/1.52 % (255066)------------------------------
% 5.25/1.52 % (255066)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.52 % (255066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.52 % (255066)CaDiCaL version: 2.1.3
% 5.25/1.52 % (255066)Termination reason: Refutation
% 5.25/1.52 % (255066)Time elapsed: 0.379 s
% 5.25/1.52 % (255066)Peak memory usage: 128 MB
% 5.25/1.52 % (255066)Instructions burned: 925 (million)
% 5.25/1.52 % (255066)------------------------------
% 5.25/1.52 % (255066)------------------------------
% 5.25/1.52 % (255060)Success in time 0.646 s
% 5.25/1.52 % Vampire exiting
%------------------------------------------------------------------------------