%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL102-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 09:37:58 AM UTC 2026
% Result : Unsatisfiable 2.29s 0.89s
% Output : Refutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 11 ( 7 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 10 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
c_in(c_Pair(v_y,v_za,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f2,negated_conjecture,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_y,v_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3,negated_conjecture,
~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),c_Comb_Ocomb_Oop_A_D_D(v_za,v_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f4,axiom,
! [X2,X0,X1] :
( c_in(c_Pair(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_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X0,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Ocontract_OAp1_0) ).
fof(f5,axiom,
! [X2,X0,X1] :
( c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(X0,X1,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X4] :
( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__trans_0) ).
fof(f9,plain,
! [X0] :
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x,v_z),X0,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X0,c_Comb_Ocomb_Oop_A_D_D(v_za,v_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(resolution,[],[f6,f3]) ).
fof(f10,plain,
~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_y,v_z),c_Comb_Ocomb_Oop_A_D_D(v_za,v_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(resolution,[],[f9,f2]) ).
fof(f16,plain,
~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_y,v_z),c_Comb_Ocomb_Oop_A_D_D(v_za,v_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(resolution,[],[f10,f5]) ).
fof(f17,plain,
~ c_in(c_Pair(v_y,v_za,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Ocontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(resolution,[],[f16,f4]) ).
fof(f20,plain,
$false,
inference(resolution,[],[f17,f1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL102-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:39:28 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 2.29/0.89 % (2056122)Input is clausal, will run a generic CNF schedule.
% 2.29/0.89 % (2056133)dis-21_1_sil=8000:lcm=predicate:random_seed=2879544970: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)
% 2.29/0.89 % (2056133)First to succeed.
% 2.29/0.89 % (2056133)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2056122"
% 2.29/0.89 % (2056128)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4240524987:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.29/0.89 % (2056130)lrs+10_1_sil=8000:sp=occurrence:random_seed=416568243:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.29/0.89 % (2056132)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4085436212:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.29/0.89 % (2056129)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=103968885:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.29/0.89 % (2056127)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=3205657529:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.29/0.89 % (2056131)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3754573273:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.29/0.89 % (2056131)Also succeeded, but the first one will report.
% 2.29/0.89 % (2056130)Also succeeded, but the first one will report.
% 2.29/0.89 % (2056132)Also succeeded, but the first one will report.
% 2.29/0.89 % (2056133)Refutation found. Thanks to Tanya!
% 2.29/0.89 % SZS status Unsatisfiable for theBenchmark
% 2.29/0.89 % SZS output start Proof for theBenchmark
% See solution above
% 2.29/0.89 % (2056133)------------------------------
% 2.29/0.89 % (2056133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.29/0.89 % (2056133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.29/0.89 % (2056133)CaDiCaL version: 2.1.3
% 2.29/0.89 % (2056133)Termination reason: Refutation
% 2.29/0.89 % (2056133)Time elapsed: 0.001 s
% 2.29/0.89 % (2056133)Peak memory usage: 88 MB
% 2.29/0.89 % (2056133)Instructions burned: 1 (million)
% 2.29/0.89 % (2056133)------------------------------
% 2.29/0.89 % (2056133)------------------------------
% 2.29/0.89 % (2056122)Success in time 0.279 s
% 2.29/0.89 % Vampire exiting
%------------------------------------------------------------------------------