%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL117-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 09:38:02 AM UTC 2026
% Result : Unsatisfiable 2.35s 0.72s
% Output : Refutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 11 unt; 2 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 19 ~; 16 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-4 aty)
% Number of variables : 8 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
c_in(c_Pair(v_z,v_w,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
c_in(c_Pair(v_x,v_x_H,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,negated_conjecture,
c_in(c_Pair(v_ya,v_y_Ha,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f4,negated_conjecture,
! [X0] :
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_x_H),v_y_Ha),v_w),X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_z)),X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f5,axiom,
! [X2,X0,X1] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,X0),X1),X2),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(X0,X2),c_Comb_Ocomb_Oop_A_D_D(X1,X2)),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__3_0) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X2,X0),c_Comb_Ocomb_Oop_A_D_D(X3,X1),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X2,X3,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X0,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__4_0) ).
fof(f7,plain,
~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_ya,v_z)),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_x_H,v_w),c_Comb_Ocomb_Oop_A_D_D(v_y_Ha,v_w)),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(resolution,[],[f5,f4]) ).
fof(f9,plain,
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_x_H,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_z),c_Comb_Ocomb_Oop_A_D_D(v_y_Ha,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(resolution,[],[f7,f6]) ).
fof(f11,definition,
( spl0_1
<=> c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_z),c_Comb_Ocomb_Oop_A_D_D(v_y_Ha,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f13,plain,
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya,v_z),c_Comb_Ocomb_Oop_A_D_D(v_y_Ha,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| spl0_1 ),
inference(avatar_component_clause,[],[f11]) ).
fof(f15,definition,
( spl0_2
<=> c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_x_H,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f17,plain,
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_x_H,v_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| spl0_2 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f18,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f9,f15,f11]) ).
fof(f27,plain,
( ~ c_in(c_Pair(v_ya,v_y_Ha,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(v_z,v_w,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| spl0_1 ),
inference(resolution,[],[f13,f6]) ).
fof(f28,plain,
( ~ c_in(c_Pair(v_z,v_w,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f27,f3]) ).
fof(f29,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f28,f1]) ).
fof(f30,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f29]) ).
fof(f31,plain,
( ~ c_in(c_Pair(v_x,v_x_H,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(v_z,v_w,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| spl0_2 ),
inference(resolution,[],[f17,f6]) ).
fof(f32,plain,
( ~ c_in(c_Pair(v_z,v_w,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f31,f2]) ).
fof(f33,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f32,f1]) ).
fof(f34,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f33]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f18]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f30]) ).
cnf(s4,plain,
spl0_2,
inference(sat_conversion,[],[f34]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3]) ).
fof(f35,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL117-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Mon Sep 28 21:40:34 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running first-order theorem proving
% 0.08/0.13 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
% 2.35/0.72 % (3809436)Input is clausal, will run a generic CNF schedule.
% 2.35/0.72 % (3809446)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1518109672:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.35/0.72 % (3809441)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=4217913335:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.35/0.72 % (3809444)lrs+10_1_sil=8000:sp=occurrence:random_seed=2808278469:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.35/0.72 % (3809445)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3383750910:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.35/0.72 % (3809443)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3358504400:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.35/0.72 % (3809442)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=612444322:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.35/0.72 % (3809447)dis-21_1_sil=8000:lcm=predicate:random_seed=75850075: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)
% 2.35/0.72 % (3809445)Also succeeded, but the first one will report.
% 2.35/0.72 % (3809447)Also succeeded, but the first one will report.
% 2.35/0.72 % (3809446)Also succeeded, but the first one will report.
% 2.35/0.72 % (3809444)First to succeed.
% 2.35/0.72 % (3809444)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3809436"
% 2.35/0.72 % (3809444)Refutation found. Thanks to Tanya!
% 2.35/0.72 % SZS status Unsatisfiable for theBenchmark
% 2.35/0.72 % SZS output start Proof for theBenchmark
% See solution above
% 2.35/0.72 % (3809444)------------------------------
% 2.35/0.72 % (3809444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/0.72 % (3809444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.72 % (3809444)CaDiCaL version: 2.1.3
% 2.35/0.72 % (3809444)Termination reason: Refutation
% 2.35/0.72 % (3809444)Time elapsed: 0.001 s
% 2.35/0.72 % (3809444)Peak memory usage: 88 MB
% 2.35/0.72 % (3809444)Instructions burned: 1 (million)
% 2.35/0.72 % (3809444)------------------------------
% 2.35/0.72 % (3809444)------------------------------
% 2.35/0.72 % (3809436)Success in time 0.297 s
% 2.35/0.72 % Vampire exiting
%------------------------------------------------------------------------------