%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : FLD050-4 : 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 : n002.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 09:49:13 AM UTC 2026
% Result : Unsatisfiable 5.07s 1.48s
% Output : Refutation 5.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 15
% Syntax : Number of formulae : 26 ( 21 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 16 ~; 10 |; 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 : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 17 ( 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ product(X3,X5,X1)
| ~ product(X4,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_1) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X1,X2)
| ~ product(X3,X4,X0)
| ~ product(X4,X1,X5)
| ~ product(X3,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_2) ).
fof(f8,axiom,
! [X0] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
fof(f9,axiom,
! [X0] :
( product(multiplicative_inverse(X0),X0,multiplicative_identity)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
fof(f10,axiom,
! [X2,X0,X1] :
( product(X0,X1,X2)
| ~ product(X1,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_multiplication) ).
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(f30,axiom,
defined(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_is_defined) ).
fof(f32,axiom,
defined(s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_is_defined) ).
fof(f33,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_7) ).
fof(f34,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_8) ).
fof(f35,negated_conjecture,
product(a,multiplicative_inverse(b),s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_9) ).
fof(f36,negated_conjecture,
product(a,d,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_10) ).
fof(f37,negated_conjecture,
product(b,c,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_11) ).
fof(f38,negated_conjecture,
~ product(c,multiplicative_inverse(d),s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_12) ).
fof(f44,plain,
product(multiplicative_inverse(b),a,s),
inference(unit_resulting_resolution,[],[f10,f35]) ).
fof(f46,plain,
~ product(multiplicative_inverse(d),c,s),
inference(unit_resulting_resolution,[],[f10,f38]) ).
fof(f80,plain,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(unit_resulting_resolution,[],[f9,f33,f28]) ).
fof(f161,plain,
product(multiplicative_identity,c,c),
inference(unit_resulting_resolution,[],[f8,f29]) ).
fof(f274,plain,
product(multiplicative_inverse(d),d,multiplicative_identity),
inference(unit_resulting_resolution,[],[f9,f34,f30]) ).
fof(f595,plain,
product(multiplicative_identity,s,s),
inference(unit_resulting_resolution,[],[f8,f32]) ).
fof(f1858,plain,
product(multiplicative_inverse(b),k,c),
inference(unit_resulting_resolution,[],[f6,f37,f80,f161]) ).
fof(f1917,plain,
~ product(d,s,c),
inference(unit_resulting_resolution,[],[f6,f46,f274,f595]) ).
fof(f1932,plain,
~ product(s,d,c),
inference(unit_resulting_resolution,[],[f10,f1917]) ).
fof(f1937,plain,
~ product(multiplicative_inverse(b),k,c),
inference(unit_resulting_resolution,[],[f7,f36,f44,f1932]) ).
fof(f1940,plain,
$false,
inference(forward_subsumption_resolution,[],[f1937,f1858]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD050-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n002.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 00:42:22 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 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
% 5.07/1.48 % (943980)Input is clausal, will run a generic CNF schedule.
% 5.07/1.48 % (943985)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=3345064222:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.07/1.48 % (943986)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=259703239:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.07/1.48 % (943988)lrs+10_1_sil=8000:sp=occurrence:random_seed=720500751:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.07/1.48 % (943987)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3211387791:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.07/1.48 % (943989)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1122363684:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.07/1.48 % (943990)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1557390496:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.07/1.48 % (943991)dis-21_1_sil=8000:lcm=predicate:random_seed=3145853641: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)
% 5.07/1.48 % (943989)Instruction limit reached!
% 5.07/1.48 % (943989)------------------------------
% 5.07/1.48 % (943989)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.48 % (943989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.48 % (943989)CaDiCaL version: 2.1.3
% 5.07/1.48 % (943989)Termination reason: Instruction limit
% 5.07/1.48 % (943989)Termination phase: Saturation
% 5.07/1.48 % (943989)Time elapsed: 0.066 s
% 5.07/1.48 % (943989)Peak memory usage: 88 MB
% 5.07/1.48 % (943989)Instructions burned: 115 (million)
% 5.07/1.48 % (943988)Instruction limit reached!
% 5.07/1.48 % (943988)------------------------------
% 5.07/1.48 % (943988)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.48 % (943988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.48 % (943988)CaDiCaL version: 2.1.3
% 5.07/1.48 % (943988)Termination reason: Instruction limit
% 5.07/1.48 % (943988)Termination phase: Saturation
% 5.07/1.48 % (943988)Time elapsed: 0.068 s
% 5.07/1.48 % (943988)Peak memory usage: 89 MB
% 5.07/1.48 % (943988)Instructions burned: 108 (million)
% 5.07/1.48 % (943991)Instruction limit reached!
% 5.07/1.48 % (943991)------------------------------
% 5.07/1.48 % (943991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.48 % (943991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.48 % (943991)CaDiCaL version: 2.1.3
% 5.07/1.48 % (943991)Termination reason: Instruction limit
% 5.07/1.48 % (943991)Termination phase: Saturation
% 5.07/1.48 % (943991)Time elapsed: 0.074 s
% 5.07/1.48 % (943991)Peak memory usage: 89 MB
% 5.07/1.48 % (943991)Instructions burned: 117 (million)
% 5.07/1.48 % (943990)Instruction limit reached!
% 5.07/1.48 % (943990)------------------------------
% 5.07/1.48 % (943990)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.48 % (943990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.48 % (943990)CaDiCaL version: 2.1.3
% 5.07/1.48 % (943990)Termination reason: Instruction limit
% 5.07/1.48 % (943990)Termination phase: Saturation
% 5.07/1.48 % (943990)Time elapsed: 0.108 s
% 5.07/1.48 % (943990)Peak memory usage: 88 MB
% 5.07/1.48 % (943990)Instructions burned: 180 (million)
% 5.07/1.48 % (943999)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=1837631277:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.07/1.48 % (944000)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=4011289191: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)
% 5.07/1.48 % (944001)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3520977641:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.07/1.48 % (944000)First to succeed.
% 5.07/1.48 % (944000)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-943980"
% 5.07/1.48 % (944002)lrs+10_64_to=lpo:sil=8000:random_seed=2718089607:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.07/1.48 % (943999)Instruction limit reached!
% 5.07/1.48 % (943999)------------------------------
% 5.07/1.48 % (943999)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.48 % (943999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.48 % (943999)CaDiCaL version: 2.1.3
% 5.07/1.48 % (943999)Termination reason: Instruction limit
% 5.07/1.48 % (943999)Termination phase: Saturation
% 5.07/1.48 % (943999)Time elapsed: 0.082 s
% 5.07/1.48 % (943999)Peak memory usage: 89 MB
% 5.07/1.48 % (943999)Instructions burned: 144 (million)
% 5.07/1.48 % (944002)Instruction limit reached!
% 5.07/1.48 % (944002)------------------------------
% 5.07/1.48 % (944002)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.48 % (944002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.48 % (944002)CaDiCaL version: 2.1.3
% 5.07/1.48 % (944002)Termination reason: Instruction limit
% 5.07/1.48 % (944002)Termination phase: Saturation
% 5.07/1.48 % (944002)Time elapsed: 0.079 s
% 5.07/1.48 % (944002)Peak memory usage: 89 MB
% 5.07/1.48 % (944002)Instructions burned: 127 (million)
% 5.07/1.48 % (943985)Also succeeded, but the first one will report.
% 5.07/1.48 % (944001)Instruction limit reached!
% 5.07/1.48 % (944001)------------------------------
% 5.07/1.48 % (944001)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.48 % (944001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.48 % (944001)CaDiCaL version: 2.1.3
% 5.07/1.48 % (944001)Termination reason: Instruction limit
% 5.07/1.48 % (944001)Termination phase: Saturation
% 5.07/1.48 % (944001)Time elapsed: 0.135 s
% 5.07/1.48 % (944001)Peak memory usage: 89 MB
% 5.07/1.48 % (944001)Instructions burned: 219 (million)
% 5.07/1.48 % (944007)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=4171058235:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.07/1.48 % (944008)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1413295154:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 5.07/1.48 % (944009)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=768959661:i=3394:sd=4:ss=included:sgt=64_2995 on theBenchmark for (2995ds/3394Mi)
% 5.07/1.48 % (944000)Refutation found. Thanks to Tanya!
% 5.07/1.48 % SZS status Unsatisfiable for theBenchmark
% 5.07/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 5.07/1.48 % (944000)------------------------------
% 5.07/1.48 % (944000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.07/1.48 % (944000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.07/1.48 % (944000)CaDiCaL version: 2.1.3
% 5.07/1.48 % (944000)Termination reason: Refutation
% 5.07/1.48 % (944000)Time elapsed: 0.029 s
% 5.07/1.48 % (944000)Peak memory usage: 89 MB
% 5.07/1.48 % (944000)Instructions burned: 56 (million)
% 5.07/1.48 % (944000)------------------------------
% 5.07/1.48 % (944000)------------------------------
% 5.07/1.48 % (943980)Success in time 0.634 s
% 5.07/1.48 % Vampire exiting
%------------------------------------------------------------------------------