%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM011-1 : 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 : n016.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 09:39:22 AM UTC 2026
% Result : Unsatisfiable 4.08s 1.38s
% Output : Refutation 4.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 9 unt; 2 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 72 ( 33 ~; 37 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 45 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f205,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_minus(X1,X2,tc_set(X3)),X3)
| c_in(X0,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).
fof(f379,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f380,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f1444,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X4,X1,tc_set(X3))
| ~ c_in(X0,c_UNITY_Oconstrains(X1,X2,X3),tc_UNITY_Oprogram(X3))
| c_in(X0,c_UNITY_Oconstrains(X4,X2,X3),tc_UNITY_Oprogram(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNITY_Oconstrains__weaken__L_0) ).
fof(f1449,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,c_WFair_Oensures(X1,X2,X3),tc_UNITY_Oprogram(X3))
| ~ c_in(X0,c_WFair_Otransient(c_minus(X1,X2,tc_set(X3)),X3),tc_UNITY_Oprogram(X3))
| ~ c_in(X0,c_UNITY_Oconstrains(c_minus(X1,X2,tc_set(X3)),c_union(X1,X2,X3),X3),tc_UNITY_Oprogram(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WFair_OensuresI_0) ).
fof(f1450,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_WFair_Oensures(X1,X2,X3),tc_UNITY_Oprogram(X3))
| c_in(X0,c_WFair_OleadsTo(X1,X2,X3),tc_UNITY_Oprogram(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WFair_OleadsTo__Basis_0) ).
fof(f1451,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,c_WFair_Otransient(X3,X2),tc_UNITY_Oprogram(X2))
| ~ c_lessequals(X3,X1,tc_set(X2))
| ~ c_in(X0,c_WFair_Otransient(X1,X2),tc_UNITY_Oprogram(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WFair_Otransient__strengthen_0) ).
fof(f1452,negated_conjecture,
c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1453,negated_conjecture,
c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1454,negated_conjecture,
~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1466,plain,
! [X2,X3,X0,X1] :
( c_in(X0,c_WFair_OleadsTo(X1,X2,X3),tc_UNITY_Oprogram(X3))
| ~ c_in(X0,c_UNITY_Oconstrains(c_minus(X1,X2,tc_set(X3)),c_union(X1,X2,X3),X3),tc_UNITY_Oprogram(X3))
| ~ c_in(X0,c_WFair_Otransient(c_minus(X1,X2,tc_set(X3)),X3),tc_UNITY_Oprogram(X3)) ),
inference(resolution,[],[f1449,f1450]) ).
fof(f1485,plain,
! [X2,X3,X0,X1,X4] :
( c_in(X3,c_UNITY_Oconstrains(X0,X4,X2),tc_UNITY_Oprogram(X2))
| ~ c_in(X3,c_UNITY_Oconstrains(X1,X4,X2),tc_UNITY_Oprogram(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(resolution,[],[f379,f1444]) ).
fof(f1486,plain,
! [X2,X3,X0,X1,X4] :
( c_in(X3,c_UNITY_Oconstrains(X0,X4,X2),tc_UNITY_Oprogram(X2))
| ~ c_in(X3,c_UNITY_Oconstrains(X1,X4,X2),tc_UNITY_Oprogram(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(resolution,[],[f380,f1444]) ).
fof(f1553,plain,
( ~ c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,v_B,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a))
| ~ c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolution,[],[f1466,f1454]) ).
fof(f1555,definition,
( spl0_1
<=> c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f1557,plain,
( ~ c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a))
| spl0_1 ),
inference(avatar_component_clause,[],[f1555]) ).
fof(f1559,definition,
( spl0_2
<=> c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,v_B,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f1561,plain,
( ~ c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,v_B,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a))
| spl0_2 ),
inference(avatar_component_clause,[],[f1559]) ).
fof(f1562,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f1553,f1559,f1555]) ).
fof(f1563,plain,
( ! [X0] :
( ~ c_in(v_F,c_WFair_Otransient(X0,t_a),tc_UNITY_Oprogram(t_a))
| ~ c_lessequals(c_minus(v_A,v_B,tc_set(t_a)),X0,tc_set(t_a)) )
| spl0_1 ),
inference(resolution,[],[f1557,f1451]) ).
fof(f1564,plain,
( ~ c_lessequals(c_minus(v_A,v_B,tc_set(t_a)),v_A,tc_set(t_a))
| spl0_1 ),
inference(resolution,[],[f1563,f1453]) ).
fof(f1566,plain,
( ~ c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),v_A,t_a),v_A,t_a)
| spl0_1 ),
inference(resolution,[],[f1564,f380]) ).
fof(f1567,plain,
( c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),v_A,t_a),c_minus(v_A,v_B,tc_set(t_a)),t_a)
| spl0_1 ),
inference(resolution,[],[f1564,f379]) ).
fof(f1569,plain,
( c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),v_A,t_a),v_A,t_a)
| spl0_1 ),
inference(resolution,[],[f1567,f205]) ).
fof(f1571,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f1569,f1566]) ).
fof(f1572,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f1571]) ).
fof(f1902,plain,
( ! [X0] :
( c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),X0,t_a),c_minus(v_A,v_B,tc_set(t_a)),t_a)
| ~ c_in(v_F,c_UNITY_Oconstrains(X0,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) )
| spl0_2 ),
inference(resolution,[],[f1485,f1561]) ).
fof(f1907,plain,
( ! [X0] :
( c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),X0,t_a),v_A,t_a)
| ~ c_in(v_F,c_UNITY_Oconstrains(X0,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) )
| spl0_2 ),
inference(resolution,[],[f1902,f205]) ).
fof(f1909,plain,
( ! [X0] :
( ~ c_in(v_F,c_UNITY_Oconstrains(X0,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a))
| ~ c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),X0,t_a),X0,t_a) )
| spl0_2 ),
inference(resolution,[],[f1486,f1561]) ).
fof(f1913,plain,
( ~ c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),v_A,t_a),v_A,t_a)
| spl0_2 ),
inference(resolution,[],[f1909,f1452]) ).
fof(f1922,plain,
( ~ c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a))
| spl0_2 ),
inference(resolution,[],[f1907,f1913]) ).
fof(f1924,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f1922,f1452]) ).
fof(f1925,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f1924]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f1562]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f1572]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f1925]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f1926,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM011-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n016.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 21:49:34 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 4.08/1.38 % (4065195)Input is clausal, will run a generic CNF schedule.
% 4.08/1.38 % (4065206)dis-21_1_sil=8000:lcm=predicate:random_seed=3177336123: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)
% 4.08/1.38 % (4065206)Instruction limit reached!
% 4.08/1.38 % (4065206)------------------------------
% 4.08/1.38 % (4065206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.38 % (4065206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.38 % (4065206)CaDiCaL version: 2.1.3
% 4.08/1.38 % (4065206)Termination reason: Instruction limit
% 4.08/1.38 % (4065206)Termination phase: Saturation
% 4.08/1.38 % (4065206)Time elapsed: 0.040 s
% 4.08/1.38 % (4065206)Peak memory usage: 89 MB
% 4.08/1.38 % (4065206)Instructions burned: 118 (million)
% 4.08/1.38 % (4065205)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3623459776:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.08/1.38 % (4065203)lrs+10_1_sil=8000:sp=occurrence:random_seed=510659973:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.08/1.38 % (4065202)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1800937493:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.08/1.38 % (4065201)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=35310477:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.08/1.38 % (4065200)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=863916058:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.08/1.38 % (4065204)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1207092344:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.08/1.38 % (4065203)Refutation not found, incomplete strategy
% 4.08/1.38 % (4065203)------------------------------
% 4.08/1.38 % (4065203)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.38 % (4065203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.38 % (4065203)CaDiCaL version: 2.1.3
% 4.08/1.38 % (4065203)Termination reason: Refutation not found, incomplete strategy
% 4.08/1.38 % (4065203)Time elapsed: 0.007 s
% 4.08/1.38 % (4065203)Peak memory usage: 89 MB
% 4.08/1.38 % (4065203)Instructions burned: 8 (million)
% 4.08/1.38 % (4065205)First to succeed.
% 4.08/1.38 % (4065205)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4065195"
% 4.08/1.38 % (4065204)Instruction limit reached!
% 4.08/1.38 % (4065204)------------------------------
% 4.08/1.38 % (4065204)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.38 % (4065204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.38 % (4065204)CaDiCaL version: 2.1.3
% 4.08/1.38 % (4065204)Termination reason: Instruction limit
% 4.08/1.38 % (4065204)Termination phase: Saturation
% 4.08/1.38 % (4065204)Time elapsed: 0.070 s
% 4.08/1.38 % (4065204)Peak memory usage: 89 MB
% 4.08/1.38 % (4065204)Instructions burned: 115 (million)
% 4.08/1.38 % (4065214)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=981474428:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 4.08/1.38 % (4065214)Instruction limit reached!
% 4.08/1.38 % (4065214)------------------------------
% 4.08/1.38 % (4065214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.38 % (4065214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.38 % (4065214)CaDiCaL version: 2.1.3
% 4.08/1.38 % (4065214)Termination reason: Instruction limit
% 4.08/1.38 % (4065214)Termination phase: Saturation
% 4.08/1.38 % (4065214)Time elapsed: 0.036 s
% 4.08/1.38 % (4065214)Peak memory usage: 89 MB
% 4.08/1.38 % (4065214)Instructions burned: 148 (million)
% 4.08/1.38 % (4065215)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=887531161: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)
% 4.08/1.38 % (4065203)------------------------------
% 4.08/1.38 % (4065203)------------------------------
% 4.08/1.38 % (4065217)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1014015388:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 4.08/1.38 % (4065217)Refutation not found, incomplete strategy
% 4.08/1.38 % (4065217)------------------------------
% 4.08/1.38 % (4065217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.38 % (4065217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.38 % (4065217)CaDiCaL version: 2.1.3
% 4.08/1.38 % (4065217)Termination reason: Refutation not found, incomplete strategy
% 4.08/1.38 % (4065217)Time elapsed: 0.003 s
% 4.08/1.38 % (4065217)Peak memory usage: 88 MB
% 4.08/1.38 % (4065217)Instructions burned: 8 (million)
% 4.08/1.38 % (4065205)Refutation found. Thanks to Tanya!
% 4.08/1.38 % SZS status Unsatisfiable for theBenchmark
% 4.08/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 4.08/1.38 % (4065205)------------------------------
% 4.08/1.38 % (4065205)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.38 % (4065205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.38 % (4065205)CaDiCaL version: 2.1.3
% 4.08/1.38 % (4065205)Termination reason: Refutation
% 4.08/1.38 % (4065205)Time elapsed: 0.049 s
% 4.08/1.38 % (4065205)Peak memory usage: 90 MB
% 4.08/1.38 % (4065205)Instructions burned: 66 (million)
% 4.08/1.38 % (4065205)------------------------------
% 4.08/1.38 % (4065205)------------------------------
% 4.08/1.38 % (4065195)Success in time 0.508 s
% 4.08/1.38 % Vampire exiting
%------------------------------------------------------------------------------