%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 09:36:32 AM UTC 2026
% Result : Unsatisfiable 0.32s 2.70s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 27 ( 18 unt; 0 def)
% Number of atoms : 48 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 24 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 39 ( 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_composition) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| defined(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_property1) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ defined(X2,X3)
| defined(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_property2) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X4] :
( ~ product(X1,X3,X4)
| ~ product(X0,X1,X2)
| ~ defined(X2,X3)
| defined(X0,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom1) ).
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/sandbox/benchmark/theBenchmark.p',category_theory_axiom2) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4] :
( ~ product(X3,X0,X4)
| ~ product(X0,X1,X2)
| ~ defined(X3,X2)
| defined(X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom4) ).
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/sandbox/benchmark/theBenchmark.p',category_theory_axiom5) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ defined(X1,X2)
| ~ defined(X0,X1)
| ~ identity_map(X1)
| defined(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom6) ).
fof(f10,axiom,
! [X0] : identity_map(domain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_is_an_identity_map) ).
fof(f14,axiom,
! [X0] : product(X0,domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_on_domain) ).
fof(f19,axiom,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_equals_c) ).
fof(f20,axiom,
! [X2,X0,X1] :
( ~ product(c,X2,X1)
| ~ product(c,X0,X1)
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product) ).
fof(f21,axiom,
product(b,h,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bh_equals_d) ).
fof(f22,axiom,
product(b,g,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_equals_d) ).
fof(f23,negated_conjecture,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).
fof(f40,plain,
defined(b,g),
inference(unit_resulting_resolution,[],[f2,f22]) ).
fof(f47,plain,
defined(domain(b),g),
inference(unit_resulting_resolution,[],[f3,f14,f40]) ).
fof(f50,plain,
defined(a,b),
inference(unit_resulting_resolution,[],[f2,f19]) ).
fof(f58,plain,
defined(c,domain(b)),
inference(unit_resulting_resolution,[],[f7,f19,f14,f50]) ).
fof(f351,plain,
defined(c,g),
inference(unit_resulting_resolution,[],[f9,f10,f58,f47]) ).
fof(f359,plain,
defined(a,d),
inference(unit_resulting_resolution,[],[f4,f22,f19,f351]) ).
fof(f374,plain,
defined(c,h),
inference(unit_resulting_resolution,[],[f7,f19,f21,f359]) ).
fof(f380,plain,
product(c,h,compose(c,h)),
inference(unit_resulting_resolution,[],[f1,f374]) ).
fof(f392,plain,
~ product(c,g,compose(c,h)),
inference(unit_resulting_resolution,[],[f20,f23,f380]) ).
fof(f400,plain,
product(a,d,compose(c,h)),
inference(unit_resulting_resolution,[],[f5,f19,f21,f380]) ).
fof(f413,plain,
~ product(a,d,compose(c,h)),
inference(unit_resulting_resolution,[],[f8,f22,f19,f392]) ).
fof(f420,plain,
$false,
inference(forward_subsumption_resolution,[],[f413,f400]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : CAT001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.27 % Computer : n008.cluster.edu
% 0.12/0.27 % Model : x86_64 x86_64
% 0.12/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.27 % Memory : 8046.5625MB
% 0.12/0.27 % OS : Linux 6.8.0-71-generic
% 0.12/0.27 % CPULimit : 300
% 0.12/0.27 % WCLimit : 300
% 0.12/0.27 % DateTime : Mon Sep 28 21:11:55 UTC 2026
% 0.12/0.28 % CPUTime :
% 0.12/0.28 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.33 Running first-order theorem proving
% 0.27/0.33 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
% 10.10/2.43 % (2656277)Input is clausal, will run a generic CNF schedule.
% 10.10/2.43 % (2656286)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2872616964:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 10.10/2.43 % (2656286)Instruction limit reached!
% 10.10/2.43 % (2656286)------------------------------
% 10.10/2.43 % (2656286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.10/2.43 % (2656286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.10/2.43 % (2656286)CaDiCaL version: 2.1.3
% 10.10/2.43 % (2656286)Termination reason: Instruction limit
% 10.10/2.43 % (2656286)Termination phase: Saturation
% 10.10/2.43 % (2656286)Time elapsed: 0.055 s
% 10.10/2.43 % (2656286)Peak memory usage: 88 MB
% 10.10/2.43 % (2656286)Instructions burned: 115 (million)
% 10.10/2.43 % (2656283)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2490452933:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 10.10/2.43 % (2656285)lrs+10_1_sil=8000:sp=occurrence:random_seed=3929751037:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 10.10/2.43 % (2656282)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=3985549513:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 10.10/2.43 % (2656284)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1089435253:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 10.10/2.43 % (2656285)Refutation not found, incomplete strategy
% 10.10/2.43 % (2656285)------------------------------
% 10.10/2.43 % (2656285)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.10/2.43 % (2656285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.10/2.43 % (2656285)CaDiCaL version: 2.1.3
% 10.10/2.43 % (2656285)Termination reason: Refutation not found, incomplete strategy
% 10.10/2.43 % (2656285)Time elapsed: 0.002 s
% 10.10/2.43 % (2656285)Peak memory usage: 88 MB
% 10.10/2.43 % (2656285)Instructions burned: 1 (million)
% 10.10/2.43 % (2656287)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4122505866:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 10.10/2.43 % (2656288)dis-21_1_sil=8000:lcm=predicate:random_seed=2260109332: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)
% 10.10/2.43 % (2656288)Instruction limit reached!
% 10.10/2.43 % (2656288)------------------------------
% 10.10/2.43 % (2656288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.10/2.43 % (2656288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.10/2.43 % (2656288)CaDiCaL version: 2.1.3
% 10.10/2.43 % (2656288)Termination reason: Instruction limit
% 10.10/2.43 % (2656288)Termination phase: Saturation
% 10.10/2.43 % (2656288)Time elapsed: 0.104 s
% 10.10/2.43 % (2656288)Peak memory usage: 88 MB
% 10.10/2.43 % (2656288)Instructions burned: 118 (million)
% 10.10/2.43 % (2656294)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=2794180271:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 10.10/2.43 % (2656294)Refutation not found, incomplete strategy
% 10.10/2.43 % (2656294)------------------------------
% 10.10/2.43 % (2656294)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.10/2.43 % (2656294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.10/2.43 % (2656294)CaDiCaL version: 2.1.3
% 10.10/2.43 % (2656294)Termination reason: Refutation not found, incomplete strategy
% 10.10/2.43 % (2656294)Time elapsed: 0.001 s
% 10.10/2.43 % (2656294)Peak memory usage: 88 MB
% 10.10/2.43 % (2656294)Instructions burned: 1 (million)
% 10.10/2.43 % (2656287)Instruction limit reached!
% 10.10/2.43 % (2656287)------------------------------
% 10.10/2.43 % (2656287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.10/2.43 % (2656287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.10/2.43 % (2656287)CaDiCaL version: 2.1.3
% 10.10/2.43 % (2656287)Termination reason: Instruction limit
% 10.10/2.43 % (2656287)Termination phase: Saturation
% 10.10/2.43 % (2656287)Time elapsed: 0.169 s
% 10.10/2.43 % (2656287)Peak memory usage: 89 MB
% 10.10/2.43 % (2656287)Instructions burned: 180 (million)
% 10.10/2.43 % (2656297)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=267258310:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 0.32/2.70 % (2656294)------------------------------
% 0.32/2.70 % (2656294)------------------------------
% 0.32/2.70 % (2656285)------------------------------
% 0.32/2.70 % (2656285)------------------------------
% 0.32/2.70 % (2656299)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=888919965:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 0.32/2.70 % (2656310)lrs+10_64_to=lpo:sil=8000:random_seed=373073528:i=126:bd=preordered_2993 on theBenchmark for (2993ds/126Mi)
% 0.32/2.70 % (2656297)Instruction limit reached!
% 0.32/2.70 % (2656297)------------------------------
% 0.32/2.70 % (2656297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.32/2.70 % (2656297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/2.70 % (2656297)CaDiCaL version: 2.1.3
% 0.32/2.70 % (2656297)Termination reason: Instruction limit
% 0.32/2.70 % (2656297)Termination phase: Saturation
% 0.32/2.70 % (2656297)Time elapsed: 0.193 s
% 0.32/2.70 % (2656297)Peak memory usage: 88 MB
% 0.32/2.70 % (2656297)Instructions burned: 189 (million)
% 0.32/2.70 % (2656310)Instruction limit reached!
% 0.32/2.70 % (2656310)------------------------------
% 0.32/2.70 % (2656310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.32/2.70 % (2656310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/2.70 % (2656310)CaDiCaL version: 2.1.3
% 0.32/2.70 % (2656310)Termination reason: Instruction limit
% 0.32/2.70 % (2656310)Termination phase: Saturation
% 0.32/2.70 % (2656310)Time elapsed: 0.070 s
% 0.32/2.70 % (2656310)Peak memory usage: 89 MB
% 0.32/2.70 % (2656310)Instructions burned: 126 (million)
% 0.32/2.70 % (2656299)Instruction limit reached!
% 0.32/2.70 % (2656299)------------------------------
% 0.32/2.70 % (2656299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.32/2.70 % (2656299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/2.70 % (2656299)CaDiCaL version: 2.1.3
% 0.32/2.70 % (2656299)Termination reason: Instruction limit
% 0.32/2.70 % (2656299)Termination phase: Saturation
% 0.32/2.70 % (2656299)Time elapsed: 0.221 s
% 0.32/2.70 % (2656299)Peak memory usage: 89 MB
% 0.32/2.70 % (2656299)Instructions burned: 219 (million)
% 0.32/2.70 % (2656312)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=172919397:avsq=on:i=194:fgj=on:bd=preordered_2993 on theBenchmark for (2993ds/194Mi)
% 0.32/2.70 % (2656315)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3895911197:i=3394:sd=4:ss=included:sgt=64_2991 on theBenchmark for (2991ds/3394Mi)
% 0.32/2.70 % (2656314)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=159559416:i=157:gtg=all_2992 on theBenchmark for (2992ds/157Mi)
% 0.32/2.70 % (2656312)Instruction limit reached!
% 0.32/2.70 % (2656312)------------------------------
% 0.32/2.70 % (2656312)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.32/2.70 % (2656312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/2.70 % (2656312)CaDiCaL version: 2.1.3
% 0.32/2.70 % (2656312)Termination reason: Instruction limit
% 0.32/2.70 % (2656312)Termination phase: Saturation
% 0.32/2.70 % (2656312)Time elapsed: 0.219 s
% 0.32/2.70 % (2656312)Peak memory usage: 89 MB
% 0.32/2.70 % (2656312)Instructions burned: 194 (million)
% 0.32/2.70 % (2656316)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=449054731:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2991 on theBenchmark for (2991ds/106Mi)
% 0.32/2.70 % (2656316)Refutation not found, incomplete strategy
% 0.32/2.70 % (2656316)------------------------------
% 0.32/2.70 % (2656316)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.32/2.70 % (2656316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/2.70 % (2656316)CaDiCaL version: 2.1.3
% 0.32/2.70 % (2656316)Termination reason: Refutation not found, incomplete strategy
% 0.32/2.70 % (2656316)Time elapsed: 0.003 s
% 0.32/2.70 % (2656316)Peak memory usage: 88 MB
% 0.32/2.70 % (2656316)Instructions burned: 1 (million)
% 0.32/2.70 % (2656283)First to succeed.
% 0.32/2.70 % (2656283)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2656277"
% 0.32/2.70 % (2656314)Instruction limit reached!
% 0.32/2.70 % (2656314)------------------------------
% 0.32/2.70 % (2656314)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.32/2.70 % (2656314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/2.70 % (2656314)CaDiCaL version: 2.1.3
% 0.32/2.70 % (2656314)Termination reason: Instruction limit
% 0.32/2.70 % (2656314)Termination phase: Saturation
% 0.32/2.70 % (2656314)Time elapsed: 0.177 s
% 0.32/2.70 % (2656314)Peak memory usage: 90 MB
% 0.32/2.70 % (2656314)Instructions burned: 157 (million)
% 0.32/2.70 % (2656320)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=529831052:i=107_2989 on theBenchmark for (2989ds/107Mi)
% 0.32/2.70 % (2656283)Refutation found. Thanks to Tanya!
% 0.32/2.70 % SZS status Unsatisfiable for theBenchmark
% 0.32/2.70 % SZS output start Proof for theBenchmark
% See solution above
% 0.32/2.70 % (2656283)------------------------------
% 0.32/2.70 % (2656283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.32/2.70 % (2656283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/2.70 % (2656283)CaDiCaL version: 2.1.3
% 0.32/2.70 % (2656283)Termination reason: Refutation
% 0.32/2.70 % (2656283)Time elapsed: 0.950 s
% 0.32/2.70 % (2656283)Peak memory usage: 128 MB
% 0.32/2.70 % (2656283)Instructions burned: 973 (million)
% 0.32/2.70 % (2656283)------------------------------
% 0.32/2.70 % (2656283)------------------------------
% 0.32/2.70 % (2656277)Success in time 1.427 s
% 0.32/2.70 % Vampire exiting
%------------------------------------------------------------------------------