%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL117-1 : 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 : 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 09:38:01 AM UTC 2026
% Result : Unsatisfiable 3.46s 1.20s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 10 unt; 2 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 21 ~; 18 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 10 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f31,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(f32,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(f1503,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(f1504,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(f1505,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(f1506,negated_conjecture,
! [X0] :
( ~ 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))
| ~ 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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1514,plain,
! [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,v_x_H),v_y_Ha),v_w),c_Comb_Ocomb_Oop_A_D_D(X0,X1),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),X1,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_x,v_z),X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(resolution,[],[f32,f1506]) ).
fof(f1525,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))
| ~ 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)) ),
inference(resolution,[],[f1514,f31]) ).
fof(f1545,definition,
( spl0_7
<=> 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_7])],[avatar_definition]) ).
fof(f1547,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_7 ),
inference(avatar_component_clause,[],[f1545]) ).
fof(f1549,definition,
( spl0_8
<=> 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_8])],[avatar_definition]) ).
fof(f1551,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_8 ),
inference(avatar_component_clause,[],[f1549]) ).
fof(f1552,plain,
( ~ spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f1525,f1549,f1545]) ).
fof(f1553,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_8 ),
inference(resolution,[],[f1551,f32]) ).
fof(f1554,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_8 ),
inference(forward_subsumption_resolution,[],[f1553,f1505]) ).
fof(f1555,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f1554,f1503]) ).
fof(f1556,plain,
spl0_8,
inference(avatar_contradiction_clause,[],[f1555]) ).
fof(f1557,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_7 ),
inference(resolution,[],[f1547,f32]) ).
fof(f1558,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_7 ),
inference(forward_subsumption_resolution,[],[f1557,f1504]) ).
fof(f1559,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f1558,f1503]) ).
fof(f1560,plain,
spl0_7,
inference(avatar_contradiction_clause,[],[f1559]) ).
cnf(s4,plain,
( ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f1552]) ).
cnf(s5,plain,
spl0_8,
inference(sat_conversion,[],[f1556]) ).
cnf(s6,plain,
spl0_7,
inference(sat_conversion,[],[f1560]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s4,s5,s6]) ).
fof(f1561,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL117-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:40:40 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.46/1.20 % (234892)Input is clausal, will run a generic CNF schedule.
% 3.46/1.20 % (234897)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=1215724964:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.46/1.20 % (234902)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2633833670:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.46/1.20 % (234898)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3307726290:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.46/1.20 % (234900)lrs+10_1_sil=8000:sp=occurrence:random_seed=538931671:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.46/1.20 % (234901)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2592610062:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.46/1.20 % (234899)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1839388026:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.46/1.20 % (234900)First to succeed.
% 3.46/1.20 % (234900)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-234892"
% 3.46/1.20 % (234901)Also succeeded, but the first one will report.
% 3.46/1.20 % (234903)dis-21_1_sil=8000:lcm=predicate:random_seed=307264217: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)
% 3.46/1.20 % (234903)Also succeeded, but the first one will report.
% 3.46/1.20 % (234902)Instruction limit reached!
% 3.46/1.20 % (234902)------------------------------
% 3.46/1.20 % (234902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.20 % (234902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.20 % (234902)CaDiCaL version: 2.1.3
% 3.46/1.20 % (234902)Termination reason: Instruction limit
% 3.46/1.20 % (234902)Termination phase: Saturation
% 3.46/1.20 % (234902)Time elapsed: 0.096 s
% 3.46/1.20 % (234902)Peak memory usage: 90 MB
% 3.46/1.20 % (234902)Instructions burned: 182 (million)
% 3.46/1.20 % (234911)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=587174293:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.46/1.20 % (234911)Also succeeded, but the first one will report.
% 3.46/1.20 % (234900)Refutation found. Thanks to Tanya!
% 3.46/1.20 % SZS status Unsatisfiable for theBenchmark
% 3.46/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.20 % (234900)------------------------------
% 3.46/1.20 % (234900)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.20 % (234900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.20 % (234900)CaDiCaL version: 2.1.3
% 3.46/1.20 % (234900)Termination reason: Refutation
% 3.46/1.20 % (234900)Time elapsed: 0.005 s
% 3.46/1.20 % (234900)Peak memory usage: 90 MB
% 3.46/1.20 % (234900)Instructions burned: 6 (million)
% 3.46/1.20 % (234900)------------------------------
% 3.46/1.20 % (234900)------------------------------
% 3.46/1.20 % (234892)Success in time 0.456 s
% 3.46/1.20 % Vampire exiting
%------------------------------------------------------------------------------