%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 09:36:34 AM UTC 2026
% Result : Unsatisfiable 0.31s 3.17s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 26 ( 19 unt; 0 def)
% Number of atoms : 40 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 18 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 28 ( 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_composition) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| defined(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_property1) ).
fof(f5,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X2,X3,X4)
| ~ product(X0,X1,X2)
| ~ product(X1,X3,X5)
| product(X0,X5,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom2) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ defined(X3,X2)
| defined(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom3) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X3,X2,X4)
| ~ product(X0,X1,X2)
| ~ product(X3,X0,X5)
| product(X5,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom5) ).
fof(f14,axiom,
! [X0] : product(X0,domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_on_domain) ).
fof(f19,axiom,
! [X2,X0,X1] :
( ~ product(X2,a,X1)
| ~ product(X0,a,X1)
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product1) ).
fof(f20,axiom,
! [X2,X0,X1] :
( ~ product(X2,b,X1)
| ~ product(X0,b,X1)
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product2) ).
fof(f21,axiom,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_equals_c) ).
fof(f22,axiom,
product(h,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hc_equals_d) ).
fof(f23,axiom,
product(g,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gc_equals_d) ).
fof(f24,negated_conjecture,
h != g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_h_equals_g) ).
fof(f43,plain,
defined(g,c),
inference(unit_resulting_resolution,[],[f2,f23]) ).
fof(f44,plain,
defined(h,c),
inference(unit_resulting_resolution,[],[f2,f22]) ).
fof(f49,plain,
defined(h,a),
inference(unit_resulting_resolution,[],[f6,f21,f44]) ).
fof(f52,plain,
product(h,a,compose(h,a)),
inference(unit_resulting_resolution,[],[f1,f49]) ).
fof(f57,plain,
defined(g,a),
inference(unit_resulting_resolution,[],[f6,f21,f43]) ).
fof(f60,plain,
product(g,a,compose(g,a)),
inference(unit_resulting_resolution,[],[f1,f57]) ).
fof(f70,plain,
product(compose(h,a),domain(a),compose(h,a)),
inference(unit_resulting_resolution,[],[f8,f14,f52,f52]) ).
fof(f72,plain,
product(compose(h,a),b,d),
inference(unit_resulting_resolution,[],[f8,f21,f22,f52]) ).
fof(f83,plain,
~ product(h,a,compose(g,a)),
inference(unit_resulting_resolution,[],[f19,f24,f60]) ).
fof(f92,plain,
product(compose(g,a),b,d),
inference(unit_resulting_resolution,[],[f8,f21,f23,f60]) ).
fof(f95,plain,
compose(h,a) = compose(g,a),
inference(unit_resulting_resolution,[],[f20,f72,f92]) ).
fof(f157,plain,
~ product(compose(h,a),domain(a),compose(g,a)),
inference(unit_resulting_resolution,[],[f5,f52,f14,f83]) ).
fof(f158,plain,
~ product(compose(h,a),domain(a),compose(h,a)),
inference(forward_demodulation,[],[f157,f95]) ).
fof(f159,plain,
$false,
inference(forward_subsumption_resolution,[],[f158,f70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.27 % Computer : n016.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8046.5625MB
% 0.09/0.27 % OS : Linux 6.8.0-71-generic
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Mon Sep 28 21:17:49 UTC 2026
% 0.09/0.28 % CPUTime :
% 0.09/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.34 Running first-order theorem proving
% 0.27/0.34 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
% 10.44/2.80 % (4021232)Input is clausal, will run a generic CNF schedule.
% 10.44/2.80 % (4021240)lrs+10_1_sil=8000:sp=occurrence:random_seed=3159547387:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 10.44/2.80 % (4021240)Refutation not found, incomplete strategy
% 10.44/2.80 % (4021240)------------------------------
% 10.44/2.80 % (4021240)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.44/2.80 % (4021240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.44/2.80 % (4021240)CaDiCaL version: 2.1.3
% 10.44/2.80 % (4021240)Termination reason: Refutation not found, incomplete strategy
% 10.44/2.80 % (4021240)Time elapsed: 0.002 s
% 10.44/2.80 % (4021240)Peak memory usage: 88 MB
% 10.44/2.80 % (4021240)Instructions burned: 1 (million)
% 10.44/2.80 % (4021237)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=1185887909:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 10.44/2.80 % (4021238)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=348394983:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 10.44/2.80 % (4021239)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1978712857:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 10.44/2.80 % (4021241)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2152420729:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 10.44/2.80 % (4021243)dis-21_1_sil=8000:lcm=predicate:random_seed=3322400041: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)
% 10.44/2.80 % (4021242)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1110657283:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 10.44/2.80 % (4021241)Instruction limit reached!
% 10.44/2.80 % (4021241)------------------------------
% 10.44/2.80 % (4021241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.44/2.80 % (4021241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.44/2.80 % (4021241)CaDiCaL version: 2.1.3
% 10.44/2.80 % (4021241)Termination reason: Instruction limit
% 10.44/2.80 % (4021241)Termination phase: Saturation
% 10.44/2.80 % (4021241)Time elapsed: 0.107 s
% 10.44/2.80 % (4021241)Peak memory usage: 88 MB
% 10.44/2.80 % (4021241)Instructions burned: 114 (million)
% 10.44/2.80 % (4021243)Instruction limit reached!
% 10.44/2.80 % (4021243)------------------------------
% 10.44/2.80 % (4021243)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.44/2.80 % (4021243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.44/2.80 % (4021243)CaDiCaL version: 2.1.3
% 10.44/2.80 % (4021243)Termination reason: Instruction limit
% 10.44/2.80 % (4021243)Termination phase: Saturation
% 10.44/2.80 % (4021243)Time elapsed: 0.108 s
% 10.44/2.80 % (4021243)Peak memory usage: 88 MB
% 10.44/2.80 % (4021243)Instructions burned: 117 (million)
% 10.44/2.80 % (4021240)------------------------------
% 10.44/2.80 % (4021240)------------------------------
% 10.44/2.80 % (4021242)Instruction limit reached!
% 10.44/2.80 % (4021242)------------------------------
% 10.44/2.80 % (4021242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.44/2.80 % (4021242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.44/2.80 % (4021242)CaDiCaL version: 2.1.3
% 10.44/2.80 % (4021242)Termination reason: Instruction limit
% 10.44/2.80 % (4021242)Termination phase: Saturation
% 10.44/2.80 % (4021242)Time elapsed: 0.187 s
% 10.44/2.80 % (4021242)Peak memory usage: 89 MB
% 10.44/2.80 % (4021242)Instructions burned: 180 (million)
% 10.44/2.80 % (4021251)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=649013132:i=143:sd=2:aac=none:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/143Mi)
% 10.44/2.80 % (4021252)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3962798245:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2995 on theBenchmark for (2995ds/189Mi)
% 10.44/2.80 % (4021251)Refutation not found, incomplete strategy
% 10.44/2.80 % (4021251)------------------------------
% 10.44/2.80 % (4021251)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.44/2.80 % (4021251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/3.17 % (4021251)CaDiCaL version: 2.1.3
% 0.31/3.17 % (4021251)Termination reason: Refutation not found, incomplete strategy
% 0.31/3.17 % (4021251)Time elapsed: 0.004 s
% 0.31/3.17 % (4021251)Peak memory usage: 88 MB
% 0.31/3.17 % (4021251)Instructions burned: 2 (million)
% 0.31/3.17 % (4021254)lrs+10_64_to=lpo:sil=8000:random_seed=2363586929:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 0.31/3.17 % (4021253)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3110417720:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 0.31/3.17 % (4021252)Instruction limit reached!
% 0.31/3.17 % (4021252)------------------------------
% 0.31/3.17 % (4021252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.31/3.17 % (4021252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/3.17 % (4021252)CaDiCaL version: 2.1.3
% 0.31/3.17 % (4021252)Termination reason: Instruction limit
% 0.31/3.17 % (4021252)Termination phase: Saturation
% 0.31/3.17 % (4021252)Time elapsed: 0.170 s
% 0.31/3.17 % (4021252)Peak memory usage: 88 MB
% 0.31/3.17 % (4021252)Instructions burned: 189 (million)
% 0.31/3.17 % (4021254)Instruction limit reached!
% 0.31/3.17 % (4021254)------------------------------
% 0.31/3.17 % (4021254)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.31/3.17 % (4021254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/3.17 % (4021254)CaDiCaL version: 2.1.3
% 0.31/3.17 % (4021254)Termination reason: Instruction limit
% 0.31/3.17 % (4021254)Termination phase: Saturation
% 0.31/3.17 % (4021254)Time elapsed: 0.131 s
% 0.31/3.17 % (4021254)Peak memory usage: 89 MB
% 0.31/3.17 % (4021254)Instructions burned: 126 (million)
% 0.31/3.17 % (4021253)Instruction limit reached!
% 0.31/3.17 % (4021253)------------------------------
% 0.31/3.17 % (4021253)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.31/3.17 % (4021253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/3.17 % (4021253)CaDiCaL version: 2.1.3
% 0.31/3.17 % (4021253)Termination reason: Instruction limit
% 0.31/3.17 % (4021253)Termination phase: Saturation
% 0.31/3.17 % (4021253)Time elapsed: 0.132 s
% 0.31/3.17 % (4021253)Peak memory usage: 89 MB
% 0.31/3.17 % (4021253)Instructions burned: 220 (million)
% 0.31/3.17 % (4021251)------------------------------
% 0.31/3.17 % (4021251)------------------------------
% 0.31/3.17 % (4021261)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3402005339:i=3394:sd=4:ss=included:sgt=64_2990 on theBenchmark for (2990ds/3394Mi)
% 0.31/3.17 % (4021259)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1482654492:avsq=on:i=194:fgj=on:bd=preordered_2991 on theBenchmark for (2991ds/194Mi)
% 0.31/3.17 % (4021260)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1764237026:i=157:gtg=all_2990 on theBenchmark for (2990ds/157Mi)
% 0.31/3.17 % (4021238)First to succeed.
% 0.31/3.17 % (4021238)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4021232"
% 0.31/3.17 % (4021260)Instruction limit reached!
% 0.31/3.17 % (4021260)------------------------------
% 0.31/3.17 % (4021260)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.31/3.17 % (4021260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/3.17 % (4021260)CaDiCaL version: 2.1.3
% 0.31/3.17 % (4021260)Termination reason: Instruction limit
% 0.31/3.17 % (4021260)Termination phase: Saturation
% 0.31/3.17 % (4021260)Time elapsed: 0.161 s
% 0.31/3.17 % (4021260)Peak memory usage: 90 MB
% 0.31/3.17 % (4021260)Instructions burned: 157 (million)
% 0.31/3.17 % (4021259)Instruction limit reached!
% 0.31/3.17 % (4021259)------------------------------
% 0.31/3.17 % (4021259)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.31/3.17 % (4021259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/3.17 % (4021259)CaDiCaL version: 2.1.3
% 0.31/3.17 % (4021259)Termination reason: Instruction limit
% 0.31/3.17 % (4021259)Termination phase: Saturation
% 0.31/3.17 % (4021259)Time elapsed: 0.216 s
% 0.31/3.17 % (4021259)Peak memory usage: 89 MB
% 0.31/3.17 % (4021259)Instructions burned: 194 (million)
% 0.31/3.17 % (4021262)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=4085460682:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2989 on theBenchmark for (2989ds/106Mi)
% 0.31/3.17 % (4021262)Refutation not found, incomplete strategy
% 0.31/3.17 % (4021262)------------------------------
% 0.31/3.17 % (4021262)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.31/3.17 % (4021262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/3.17 % (4021262)CaDiCaL version: 2.1.3
% 0.31/3.17 % (4021262)Termination reason: Refutation not found, incomplete strategy
% 0.31/3.17 % (4021262)Time elapsed: 0.003 s
% 0.31/3.17 % (4021262)Peak memory usage: 88 MB
% 0.31/3.17 % (4021262)Instructions burned: 1 (million)
% 0.31/3.17 % (4021266)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=809653665:i=107_2986 on theBenchmark for (2986ds/107Mi)
% 0.31/3.17 % (4021267)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=3036781586:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2986 on theBenchmark for (2986ds/242Mi)
% 0.31/3.17 % (4021238)Refutation found. Thanks to Tanya!
% 0.31/3.17 % SZS status Unsatisfiable for theBenchmark
% 0.31/3.17 % SZS output start Proof for theBenchmark
% See solution above
% 0.31/3.18 % (4021238)------------------------------
% 0.31/3.18 % (4021238)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.31/3.18 % (4021238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/3.18 % (4021238)CaDiCaL version: 2.1.3
% 0.31/3.18 % (4021238)Termination reason: Refutation
% 0.31/3.18 % (4021238)Time elapsed: 0.991 s
% 0.31/3.18 % (4021238)Peak memory usage: 127 MB
% 0.31/3.18 % (4021238)Instructions burned: 929 (million)
% 0.31/3.18 % (4021238)------------------------------
% 0.31/3.18 % (4021238)------------------------------
% 0.31/3.18 % (4021232)Success in time 1.702 s
% 0.31/3.18 % Vampire exiting
%------------------------------------------------------------------------------