%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD032-1 : 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 : n006.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 09:49:06 AM UTC 2026
% Result : Unsatisfiable 5.15s 1.44s
% Output : Refutation 5.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 27 ( 8 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 76 ( 44 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( equalish(multiply(multiplicative_identity,X0),X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
fof(f7,axiom,
! [X0] :
( equalish(multiply(X0,multiplicative_inverse(X0)),multiplicative_identity)
| ~ defined(X0)
| equalish(X0,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
fof(f8,axiom,
! [X0,X1] :
( equalish(multiply(X0,X1),multiply(X1,X0))
| ~ defined(X0)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_multiplication) ).
fof(f15,axiom,
! [X0] :
( defined(multiplicative_inverse(X0))
| ~ defined(X0)
| equalish(X0,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
fof(f22,axiom,
! [X0,X1] :
( equalish(X0,X1)
| ~ equalish(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_equality) ).
fof(f23,axiom,
! [X2,X0,X1] :
( equalish(X0,X1)
| ~ equalish(X0,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_equality) ).
fof(f25,axiom,
! [X2,X0,X1] :
( equalish(multiply(X0,X1),multiply(X2,X1))
| ~ defined(X1)
| ~ equalish(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_multiplication) ).
fof(f28,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f29,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_2) ).
fof(f30,negated_conjecture,
equalish(multiplicative_inverse(a),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverses_equal) ).
fof(f31,negated_conjecture,
~ equalish(a,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_multiplicative_identity_4) ).
fof(f35,plain,
! [X0] :
( ~ equalish(a,X0)
| ~ equalish(X0,multiplicative_identity) ),
inference(resolution,[],[f31,f23]) ).
fof(f44,plain,
! [X0] :
( ~ equalish(X0,a)
| ~ equalish(X0,multiplicative_identity) ),
inference(resolution,[],[f35,f22]) ).
fof(f63,plain,
( ~ equalish(multiply(multiplicative_identity,a),multiplicative_identity)
| ~ defined(a) ),
inference(resolution,[],[f44,f6]) ).
fof(f64,plain,
~ equalish(multiply(multiplicative_identity,a),multiplicative_identity),
inference(forward_subsumption_resolution,[],[f63,f28]) ).
fof(f81,plain,
! [X0] :
( ~ equalish(multiply(multiplicative_identity,a),X0)
| ~ equalish(X0,multiplicative_identity) ),
inference(resolution,[],[f64,f23]) ).
fof(f166,plain,
! [X0] :
( ~ equalish(multiply(X0,a),multiplicative_identity)
| ~ defined(a)
| ~ equalish(multiplicative_identity,X0) ),
inference(resolution,[],[f81,f25]) ).
fof(f173,plain,
! [X0] :
( ~ equalish(multiply(X0,a),multiplicative_identity)
| ~ equalish(multiplicative_identity,X0) ),
inference(forward_subsumption_resolution,[],[f166,f28]) ).
fof(f417,plain,
! [X0,X1] :
( ~ equalish(multiply(X0,a),X1)
| ~ equalish(multiplicative_identity,X0)
| ~ equalish(X1,multiplicative_identity) ),
inference(resolution,[],[f173,f23]) ).
fof(f1131,plain,
! [X0] :
( ~ equalish(multiplicative_identity,X0)
| ~ equalish(multiply(a,X0),multiplicative_identity)
| ~ defined(X0)
| ~ defined(a) ),
inference(resolution,[],[f417,f8]) ).
fof(f1136,plain,
! [X0] :
( ~ equalish(multiply(a,X0),multiplicative_identity)
| ~ equalish(multiplicative_identity,X0)
| ~ defined(X0) ),
inference(forward_subsumption_resolution,[],[f1131,f28]) ).
fof(f1965,plain,
( ~ equalish(multiplicative_identity,multiplicative_inverse(a))
| ~ defined(multiplicative_inverse(a))
| ~ defined(a)
| equalish(a,additive_identity) ),
inference(resolution,[],[f1136,f7]) ).
fof(f1968,plain,
( ~ equalish(multiplicative_identity,multiplicative_inverse(a))
| ~ defined(a)
| equalish(a,additive_identity) ),
inference(forward_subsumption_resolution,[],[f1965,f15]) ).
fof(f1969,plain,
( ~ equalish(multiplicative_identity,multiplicative_inverse(a))
| equalish(a,additive_identity) ),
inference(forward_subsumption_resolution,[],[f1968,f28]) ).
fof(f1970,plain,
~ equalish(multiplicative_identity,multiplicative_inverse(a)),
inference(forward_subsumption_resolution,[],[f1969,f29]) ).
fof(f1971,plain,
~ equalish(multiplicative_inverse(a),multiplicative_identity),
inference(resolution,[],[f1970,f22]) ).
fof(f1973,plain,
$false,
inference(forward_subsumption_resolution,[],[f1971,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD032-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n006.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 00:30:25 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 5.15/1.44 % (360958)Input is clausal, will run a generic CNF schedule.
% 5.15/1.44 % (360965)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3780714106:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.15/1.44 % (360969)dis-21_1_sil=8000:lcm=predicate:random_seed=676036679: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)
% 5.15/1.44 % (360964)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=369566186:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.15/1.44 % (360967)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1702108803:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.15/1.44 % (360963)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=2357978567:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.15/1.44 % (360966)lrs+10_1_sil=8000:sp=occurrence:random_seed=3950147331:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.15/1.44 % (360968)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3461464627:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.15/1.44 % (360967)Instruction limit reached!
% 5.15/1.44 % (360967)------------------------------
% 5.15/1.44 % (360967)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.15/1.44 % (360967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.15/1.44 % (360967)CaDiCaL version: 2.1.3
% 5.15/1.44 % (360967)Termination reason: Instruction limit
% 5.15/1.44 % (360967)Termination phase: Saturation
% 5.15/1.44 % (360967)Time elapsed: 0.070 s
% 5.15/1.44 % (360967)Peak memory usage: 88 MB
% 5.15/1.44 % (360967)Instructions burned: 115 (million)
% 5.15/1.44 % (360969)Instruction limit reached!
% 5.15/1.44 % (360969)------------------------------
% 5.15/1.44 % (360969)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.15/1.44 % (360969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.15/1.44 % (360969)CaDiCaL version: 2.1.3
% 5.15/1.44 % (360969)Termination reason: Instruction limit
% 5.15/1.44 % (360969)Termination phase: Saturation
% 5.15/1.44 % (360969)Time elapsed: 0.073 s
% 5.15/1.44 % (360969)Peak memory usage: 89 MB
% 5.15/1.44 % (360969)Instructions burned: 118 (million)
% 5.15/1.44 % (360966)Instruction limit reached!
% 5.15/1.44 % (360966)------------------------------
% 5.15/1.44 % (360966)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.15/1.44 % (360966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.15/1.44 % (360966)CaDiCaL version: 2.1.3
% 5.15/1.44 % (360966)Termination reason: Instruction limit
% 5.15/1.44 % (360966)Termination phase: Saturation
% 5.15/1.44 % (360966)Time elapsed: 0.067 s
% 5.15/1.44 % (360966)Peak memory usage: 89 MB
% 5.15/1.44 % (360966)Instructions burned: 107 (million)
% 5.15/1.44 % (360968)Instruction limit reached!
% 5.15/1.44 % (360968)------------------------------
% 5.15/1.44 % (360968)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.15/1.44 % (360968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.15/1.44 % (360968)CaDiCaL version: 2.1.3
% 5.15/1.44 % (360968)Termination reason: Instruction limit
% 5.15/1.44 % (360968)Termination phase: Saturation
% 5.15/1.44 % (360968)Time elapsed: 0.117 s
% 5.15/1.44 % (360968)Peak memory usage: 89 MB
% 5.15/1.44 % (360968)Instructions burned: 181 (million)
% 5.15/1.44 % (360978)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1180285506: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)
% 5.15/1.44 % (360977)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=3715454589:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.15/1.44 % (360979)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=717319044:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.15/1.44 % (360979)First to succeed.
% 5.15/1.44 % (360979)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-360958"
% 5.15/1.44 % (360980)lrs+10_64_to=lpo:sil=8000:random_seed=573720784:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.15/1.44 % (360977)Instruction limit reached!
% 5.15/1.44 % (360977)------------------------------
% 5.15/1.44 % (360977)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.15/1.44 % (360977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.15/1.44 % (360977)CaDiCaL version: 2.1.3
% 5.15/1.44 % (360977)Termination reason: Instruction limit
% 5.15/1.44 % (360977)Termination phase: Saturation
% 5.15/1.44 % (360977)Time elapsed: 0.082 s
% 5.15/1.44 % (360977)Peak memory usage: 89 MB
% 5.15/1.44 % (360977)Instructions burned: 143 (million)
% 5.15/1.44 % (360978)Instruction limit reached!
% 5.15/1.44 % (360978)------------------------------
% 5.15/1.44 % (360978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.15/1.44 % (360978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.15/1.44 % (360978)CaDiCaL version: 2.1.3
% 5.15/1.44 % (360978)Termination reason: Instruction limit
% 5.15/1.44 % (360978)Termination phase: Saturation
% 5.15/1.44 % (360978)Time elapsed: 0.096 s
% 5.15/1.44 % (360978)Peak memory usage: 94 MB
% 5.15/1.44 % (360978)Instructions burned: 190 (million)
% 5.15/1.44 % (360980)Instruction limit reached!
% 5.15/1.44 % (360980)------------------------------
% 5.15/1.44 % (360980)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.15/1.44 % (360980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.15/1.44 % (360980)CaDiCaL version: 2.1.3
% 5.15/1.44 % (360980)Termination reason: Instruction limit
% 5.15/1.44 % (360980)Termination phase: Saturation
% 5.15/1.44 % (360980)Time elapsed: 0.078 s
% 5.15/1.44 % (360980)Peak memory usage: 89 MB
% 5.15/1.44 % (360980)Instructions burned: 126 (million)
% 5.15/1.44 % (360965)Also succeeded, but the first one will report.
% 5.15/1.44 % (360985)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2000943412:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.15/1.44 % (360986)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3011991446:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 5.15/1.44 % (360987)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1501144670:i=3394:sd=4:ss=included:sgt=64_2995 on theBenchmark for (2995ds/3394Mi)
% 5.15/1.44 % (360985)Instruction limit reached!
% 5.15/1.44 % (360985)------------------------------
% 5.15/1.44 % (360985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.15/1.44 % (360985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.15/1.44 % (360985)CaDiCaL version: 2.1.3
% 5.15/1.44 % (360985)Termination reason: Instruction limit
% 5.15/1.44 % (360985)Termination phase: Saturation
% 5.15/1.44 % (360985)Time elapsed: 0.084 s
% 5.15/1.44 % (360985)Peak memory usage: 88 MB
% 5.15/1.44 % (360985)Instructions burned: 195 (million)
% 5.15/1.44 % (360979)Refutation found. Thanks to Tanya!
% 5.15/1.44 % SZS status Unsatisfiable for theBenchmark
% 5.15/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 5.15/1.44 % (360979)------------------------------
% 5.15/1.44 % (360979)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.15/1.44 % (360979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.15/1.44 % (360979)CaDiCaL version: 2.1.3
% 5.15/1.44 % (360979)Termination reason: Refutation
% 5.15/1.44 % (360979)Time elapsed: 0.040 s
% 5.15/1.44 % (360979)Peak memory usage: 88 MB
% 5.15/1.44 % (360979)Instructions burned: 68 (million)
% 5.15/1.44 % (360979)------------------------------
% 5.15/1.44 % (360979)------------------------------
% 5.15/1.44 % (360958)Success in time 0.654 s
% 5.15/1.44 % Vampire exiting
%------------------------------------------------------------------------------