%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD068-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 09:49:20 AM UTC 2026
% Result : Unsatisfiable 0.19s 1.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 11
% Syntax : Number of formulae : 20 ( 13 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 27 ( 15 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X0,X1,X2)
| ~ sum(X3,X4,X0)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X5,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_addition_2) ).
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f4,axiom,
! [X0] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f5,axiom,
! [X2,X0,X1] :
( sum(X0,X1,X2)
| ~ sum(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f15,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f19,axiom,
! [X0,X1] :
( sum(X0,X1,add(X0,X1))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_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/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,negated_conjecture,
less_or_equal(additive_identity,add(b,additive_inverse(a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).
fof(f30,negated_conjecture,
~ less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_4) ).
fof(f31,plain,
sum(additive_identity,a,a),
inference(unit_resulting_resolution,[],[f3,f27]) ).
fof(f32,plain,
sum(additive_inverse(a),a,additive_identity),
inference(unit_resulting_resolution,[],[f4,f27]) ).
fof(f40,plain,
defined(additive_inverse(a)),
inference(unit_resulting_resolution,[],[f15,f27]) ).
fof(f59,plain,
sum(additive_identity,b,b),
inference(unit_resulting_resolution,[],[f3,f28]) ).
fof(f130,plain,
sum(b,additive_inverse(a),add(b,additive_inverse(a))),
inference(unit_resulting_resolution,[],[f19,f28,f40]) ).
fof(f194,plain,
~ sum(add(b,additive_inverse(a)),a,b),
inference(unit_resulting_resolution,[],[f24,f30,f29,f31]) ).
fof(f402,plain,
sum(b,additive_identity,b),
inference(unit_resulting_resolution,[],[f5,f59]) ).
fof(f1188,plain,
~ sum(b,additive_inverse(a),add(b,additive_inverse(a))),
inference(unit_resulting_resolution,[],[f2,f194,f32,f402]) ).
fof(f1193,plain,
$false,
inference(forward_subsumption_resolution,[],[f1188,f130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD068-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n009.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
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 00:48:30 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 0.19/1.50 % (3665582)Input is clausal, will run a generic CNF schedule.
% 0.19/1.50 % (3665588)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4135032111:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.19/1.50 % (3665587)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=1192864755:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.19/1.50 % (3665592)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=972078390:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.19/1.50 % (3665593)dis-21_1_sil=8000:lcm=predicate:random_seed=3171794399: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)
% 0.19/1.50 % (3665591)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3311169773:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.19/1.50 % (3665590)lrs+10_1_sil=8000:sp=occurrence:random_seed=2871730455:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.19/1.50 % (3665589)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=857369623:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.19/1.50 % (3665591)Instruction limit reached!
% 0.19/1.50 % (3665591)------------------------------
% 0.19/1.50 % (3665591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (3665591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (3665591)CaDiCaL version: 2.1.3
% 0.19/1.50 % (3665591)Termination reason: Instruction limit
% 0.19/1.50 % (3665591)Termination phase: Saturation
% 0.19/1.50 % (3665591)Time elapsed: 0.061 s
% 0.19/1.50 % (3665591)Peak memory usage: 88 MB
% 0.19/1.50 % (3665591)Instructions burned: 114 (million)
% 0.19/1.50 % (3665590)Instruction limit reached!
% 0.19/1.50 % (3665590)------------------------------
% 0.19/1.50 % (3665590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (3665590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (3665590)CaDiCaL version: 2.1.3
% 0.19/1.50 % (3665590)Termination reason: Instruction limit
% 0.19/1.50 % (3665590)Termination phase: Saturation
% 0.19/1.50 % (3665590)Time elapsed: 0.064 s
% 0.19/1.50 % (3665590)Peak memory usage: 88 MB
% 0.19/1.50 % (3665590)Instructions burned: 107 (million)
% 0.19/1.50 % (3665593)Instruction limit reached!
% 0.19/1.50 % (3665593)------------------------------
% 0.19/1.50 % (3665593)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (3665593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (3665593)CaDiCaL version: 2.1.3
% 0.19/1.50 % (3665593)Termination reason: Instruction limit
% 0.19/1.50 % (3665593)Termination phase: Saturation
% 0.19/1.50 % (3665593)Time elapsed: 0.069 s
% 0.19/1.50 % (3665593)Peak memory usage: 89 MB
% 0.19/1.50 % (3665593)Instructions burned: 118 (million)
% 0.19/1.50 % (3665592)Instruction limit reached!
% 0.19/1.50 % (3665592)------------------------------
% 0.19/1.50 % (3665592)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (3665592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (3665592)CaDiCaL version: 2.1.3
% 0.19/1.50 % (3665592)Termination reason: Instruction limit
% 0.19/1.50 % (3665592)Termination phase: Saturation
% 0.19/1.50 % (3665592)Time elapsed: 0.121 s
% 0.19/1.50 % (3665592)Peak memory usage: 89 MB
% 0.19/1.50 % (3665592)Instructions burned: 180 (million)
% 0.19/1.50 % (3665601)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=1119683718:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.19/1.50 % (3665602)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=359628624: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)
% 0.19/1.50 % (3665602)First to succeed.
% 0.19/1.50 % (3665602)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3665582"
% 0.19/1.50 % (3665603)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2181305693:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 0.19/1.50 % (3665601)Instruction limit reached!
% 0.19/1.50 % (3665601)------------------------------
% 0.19/1.50 % (3665601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (3665601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (3665601)CaDiCaL version: 2.1.3
% 0.19/1.50 % (3665601)Termination reason: Instruction limit
% 0.19/1.50 % (3665601)Termination phase: Saturation
% 0.19/1.50 % (3665601)Time elapsed: 0.058 s
% 0.19/1.50 % (3665601)Peak memory usage: 87 MB
% 0.19/1.50 % (3665601)Instructions burned: 144 (million)
% 0.19/1.50 % (3665604)lrs+10_64_to=lpo:sil=8000:random_seed=3150923095:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 0.19/1.50 % (3665603)Instruction limit reached!
% 0.19/1.50 % (3665603)------------------------------
% 0.19/1.50 % (3665603)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (3665603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (3665603)CaDiCaL version: 2.1.3
% 0.19/1.50 % (3665603)Termination reason: Instruction limit
% 0.19/1.50 % (3665603)Termination phase: Saturation
% 0.19/1.50 % (3665603)Time elapsed: 0.077 s
% 0.19/1.50 % (3665603)Peak memory usage: 87 MB
% 0.19/1.50 % (3665603)Instructions burned: 220 (million)
% 0.19/1.50 % (3665588)Also succeeded, but the first one will report.
% 0.19/1.50 % (3665604)Instruction limit reached!
% 0.19/1.50 % (3665604)------------------------------
% 0.19/1.50 % (3665604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (3665604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (3665604)CaDiCaL version: 2.1.3
% 0.19/1.50 % (3665604)Termination reason: Instruction limit
% 0.19/1.50 % (3665604)Termination phase: Saturation
% 0.19/1.50 % (3665604)Time elapsed: 0.056 s
% 0.19/1.50 % (3665604)Peak memory usage: 87 MB
% 0.19/1.50 % (3665604)Instructions burned: 128 (million)
% 0.19/1.50 % (3665608)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=508404787:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 0.19/1.50 % (3665602)Refutation found. Thanks to Tanya!
% 0.19/1.50 % SZS status Unsatisfiable for theBenchmark
% 0.19/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.50 % (3665602)------------------------------
% 0.19/1.50 % (3665602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (3665602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (3665602)CaDiCaL version: 2.1.3
% 0.19/1.50 % (3665602)Termination reason: Refutation
% 0.19/1.50 % (3665602)Time elapsed: 0.015 s
% 0.19/1.50 % (3665602)Peak memory usage: 88 MB
% 0.19/1.50 % (3665602)Instructions burned: 25 (million)
% 0.19/1.50 % (3665602)------------------------------
% 0.19/1.50 % (3665602)------------------------------
% 0.19/1.50 % (3665582)Success in time 0.645 s
% 0.19/1.50 % Vampire exiting
%------------------------------------------------------------------------------