%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL121-1 : 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 : n010.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 3.97s 1.44s
% Output : Refutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 24 ( 7 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 61 ( 35 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f393,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(f1445,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Comb_Odiamond(X0,X1)
| ~ c_in(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
| c_in(c_Pair(X3,c_Comb_Odiamond__strip__lemmaE__1(X0,X4,X3,X1),X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_0) ).
fof(f1446,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Comb_Odiamond(X0,X1)
| ~ c_in(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
| c_in(c_Pair(X4,c_Comb_Odiamond__strip__lemmaE__1(X0,X4,X3,X1),X1,X1),X0,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_1) ).
fof(f1447,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(f1448,negated_conjecture,
c_Comb_Odiamond(v_r,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1450,negated_conjecture,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1451,negated_conjecture,
c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1452,negated_conjecture,
! [X0] :
( c_in(c_Pair(v_ya,v_x(X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f1453,negated_conjecture,
! [X0] :
( c_in(c_Pair(X0,v_x(X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f1454,negated_conjecture,
! [X0] :
( ~ c_in(c_Pair(v_xaa,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f1483,plain,
! [X0,X1] :
( ~ c_in(c_Pair(v_xaa,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[],[f1447,f1454]) ).
fof(f1499,plain,
! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X2,c_Comb_Odiamond__strip__lemmaE__1(v_r,X2,X1,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[],[f1446,f1448]) ).
fof(f1502,plain,
! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,X2,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X1,c_Comb_Odiamond__strip__lemmaE__1(v_r,X2,X1,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[],[f1445,f1448]) ).
fof(f1544,plain,
! [X0] :
( ~ c_in(c_Pair(v_x(v_xaa),X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[],[f1483,f1453]) ).
fof(f1549,plain,
! [X0] :
( ~ c_in(c_Pair(v_x(v_xaa),X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(forward_subsumption_resolution,[],[f1544,f1451]) ).
fof(f1550,plain,
! [X0] :
( ~ c_in(c_Pair(v_ya,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| c_in(c_Pair(X0,c_Comb_Odiamond__strip__lemmaE__1(v_r,X0,v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[],[f1499,f1450]) ).
fof(f1551,plain,
! [X0] :
( c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,X0,v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_ya,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[],[f1502,f1450]) ).
fof(f1555,plain,
! [X0] :
( ~ c_in(c_Pair(v_x(v_xaa),X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[],[f1549,f393]) ).
fof(f1594,plain,
! [X0] :
( c_in(c_Pair(v_x(X0),c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(X0),v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[],[f1550,f1452]) ).
fof(f1734,plain,
( ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[],[f1594,f1555]) ).
fof(f1743,plain,
~ c_in(c_Pair(v_z,c_Comb_Odiamond__strip__lemmaE__1(v_r,v_x(v_xaa),v_z,t_a),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(forward_subsumption_resolution,[],[f1734,f1451]) ).
fof(f1747,plain,
~ c_in(c_Pair(v_ya,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolution,[],[f1743,f1551]) ).
fof(f1754,plain,
~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
inference(resolution,[],[f1747,f1452]) ).
fof(f1757,plain,
$false,
inference(forward_subsumption_resolution,[],[f1754,f1451]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL121-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n010.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 21:41:32 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running first-order theorem proving
% 0.09/0.25 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
% 3.97/1.44 % (2383435)Input is clausal, will run a generic CNF schedule.
% 3.97/1.44 % (2383449)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=4056763495:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.97/1.44 % (2383451)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3921651018:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.97/1.44 % (2383454)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=990928397:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.97/1.44 % (2383450)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2028314242:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.97/1.44 % (2383452)lrs+10_1_sil=8000:sp=occurrence:random_seed=1539687152:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.97/1.44 % (2383455)dis-21_1_sil=8000:lcm=predicate:random_seed=2713724525: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)
% 3.97/1.44 % (2383453)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2742799949:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.97/1.44 % (2383454)First to succeed.
% 3.97/1.44 % (2383454)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2383435"
% 3.97/1.44 % (2383453)Also succeeded, but the first one will report.
% 3.97/1.44 % (2383452)Instruction limit reached!
% 3.97/1.44 % (2383452)------------------------------
% 3.97/1.44 % (2383452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.44 % (2383452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.44 % (2383452)CaDiCaL version: 2.1.3
% 3.97/1.44 % (2383452)Termination reason: Instruction limit
% 3.97/1.44 % (2383452)Termination phase: Saturation
% 3.97/1.44 % (2383452)Time elapsed: 0.066 s
% 3.97/1.44 % (2383452)Peak memory usage: 89 MB
% 3.97/1.44 % (2383452)Instructions burned: 114 (million)
% 3.97/1.44 % (2383455)Instruction limit reached!
% 3.97/1.44 % (2383455)------------------------------
% 3.97/1.44 % (2383455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.44 % (2383455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.44 % (2383455)CaDiCaL version: 2.1.3
% 3.97/1.44 % (2383455)Termination reason: Instruction limit
% 3.97/1.44 % (2383455)Termination phase: Saturation
% 3.97/1.44 % (2383455)Time elapsed: 0.069 s
% 3.97/1.44 % (2383455)Peak memory usage: 89 MB
% 3.97/1.44 % (2383455)Instructions burned: 117 (million)
% 3.97/1.44 % (2383464)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=4182597162:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.97/1.44 % (2383463)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=2751220634:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.97/1.44 % (2383454)Refutation found. Thanks to Tanya!
% 3.97/1.44 % SZS status Unsatisfiable for theBenchmark
% 3.97/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.97/1.44 % (2383454)------------------------------
% 3.97/1.44 % (2383454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.44 % (2383454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.44 % (2383454)CaDiCaL version: 2.1.3
% 3.97/1.44 % (2383454)Termination reason: Refutation
% 3.97/1.44 % (2383454)Time elapsed: 0.036 s
% 3.97/1.44 % (2383454)Peak memory usage: 89 MB
% 3.97/1.44 % (2383454)Instructions burned: 56 (million)
% 3.97/1.44 % (2383454)------------------------------
% 3.97/1.44 % (2383454)------------------------------
% 3.97/1.44 % (2383435)Success in time 0.479 s
% 3.97/1.44 % Vampire exiting
%------------------------------------------------------------------------------