%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL090-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 09:37:54 AM UTC 2026
% Result : Unsatisfiable 3.53s 1.06s
% Output : Refutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 66 ( 20 unt; 7 def)
% Number of atoms : 135 ( 21 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 124 ( 55 ~; 62 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 8 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
combK != combS,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_s) ).
fof(f3,axiom,
! [X0,X1] : combS != comb_app(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_app) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( comb_app(X0,X1) != comb_app(X2,X3)
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app_app1) ).
fof(f15,axiom,
! [X2,X0,X1] :
( ap_contractE_c1(X0,X1,X2)
| ~ member(pair(comb_app(X0,X1),X2),contract)
| ap_contractE_c2(X0,X1,X2)
| ap_contractE_c3(X0,X1,X2)
| ap_contractE_c4(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE1) ).
fof(f18,axiom,
! [X2,X0,X1] :
( ~ ap_contractE_c1(X0,X1,X2)
| X0 = comb_app(combK,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE4) ).
fof(f19,plain,
! [X2,X0,X1] :
( ~ ap_contractE_c1(X0,X1,X2)
| comb_app(combK,X2) = X0 ),
inference(reorient_equations,[],[f18]) ).
fof(f25,axiom,
! [X2,X0,X1] :
( ~ ap_contractE_c2(X0,X1,X2)
| X0 = comb_app(comb_app(combS,ap_contractE_sk1p(X0,X1,X2)),ap_contractE_sk1q(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE9) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ ap_contractE_c2(X0,X1,X2)
| comb_app(comb_app(combS,ap_contractE_sk1p(X0,X1,X2)),ap_contractE_sk1q(X0,X1,X2)) = X0 ),
inference(reorient_equations,[],[f25]) ).
fof(f27,axiom,
! [X2,X0,X1] :
( ~ ap_contractE_c3(X0,X1,X2)
| member(pair(X0,ap_contractE_sk2q(X0,X1,X2)),contract) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE10) ).
fof(f31,axiom,
! [X2,X0,X1] :
( ~ ap_contractE_c4(X0,X1,X2)
| member(pair(X1,ap_contractE_sk3q(X0,X1,X2)),contract) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_contractE13) ).
fof(f35,axiom,
! [X0] : ~ member(pair(combK,X0),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_contractE) ).
fof(f36,axiom,
! [X0] : ~ member(pair(combS,X0),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_contractE) ).
fof(f37,negated_conjecture,
member(pair(comb_app(comb_app(combS,combK),combK),r),contract),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_contract_E) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ member(pair(comb_app(X0,X1),X2),contract)
| ap_contractE_c2(X0,X1,X2)
| ap_contractE_c3(X0,X1,X2)
| ap_contractE_c4(X0,X1,X2)
| comb_app(combK,X2) = X0 ),
inference(resolution,[],[f15,f19]) ).
fof(f43,plain,
( ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c3(comb_app(combS,combK),combK,r)
| ap_contractE_c4(comb_app(combS,combK),combK,r)
| comb_app(combS,combK) = comb_app(combK,r) ),
inference(resolution,[],[f42,f37]) ).
fof(f46,definition,
( spl0_1
<=> comb_app(combS,combK) = comb_app(combK,r) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f48,plain,
( comb_app(combS,combK) = comb_app(combK,r)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f50,definition,
( spl0_2
<=> ap_contractE_c4(comb_app(combS,combK),combK,r) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f52,plain,
( ap_contractE_c4(comb_app(combS,combK),combK,r)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f54,definition,
( spl0_3
<=> ap_contractE_c3(comb_app(combS,combK),combK,r) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f56,plain,
( ap_contractE_c3(comb_app(combS,combK),combK,r)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f58,definition,
( spl0_4
<=> ap_contractE_c2(comb_app(combS,combK),combK,r) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f60,plain,
( ap_contractE_c2(comb_app(combS,combK),combK,r)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f43,f58,f54,f50,f46]) ).
fof(f64,plain,
( member(pair(combK,ap_contractE_sk3q(comb_app(combS,combK),combK,r)),contract)
| ~ spl0_2 ),
inference(resolution,[],[f52,f31]) ).
fof(f65,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f64,f35]) ).
fof(f66,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f65]) ).
fof(f116,definition,
( spl0_11
<=> ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f118,plain,
( ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f120,definition,
( spl0_12
<=> ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f122,plain,
( ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f124,definition,
( spl0_13
<=> ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f126,plain,
( ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f135,plain,
( ! [X0,X1] :
( comb_app(X0,X1) != comb_app(combK,r)
| combS = X0 )
| ~ spl0_1 ),
inference(superposition,[],[f4,f48]) ).
fof(f160,plain,
( combK = combS
| ~ spl0_1 ),
inference(equality_resolution,[],[f135]) ).
fof(f161,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f160,f1]) ).
fof(f162,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f161]) ).
fof(f335,plain,
( member(pair(comb_app(combS,combK),ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract)
| ~ spl0_3 ),
inference(resolution,[],[f56,f27]) ).
fof(f350,plain,
( ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| combS = comb_app(combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ~ spl0_3 ),
inference(resolution,[],[f335,f42]) ).
fof(f351,plain,
( ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f350,f3]) ).
fof(f352,plain,
( spl0_11
| spl0_12
| spl0_13
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f351,f54,f124,f120,f116]) ).
fof(f358,plain,
( member(pair(combK,ap_contractE_sk3q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract)
| ~ spl0_11 ),
inference(resolution,[],[f118,f31]) ).
fof(f359,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f358,f35]) ).
fof(f360,plain,
~ spl0_11,
inference(avatar_contradiction_clause,[],[f359]) ).
fof(f362,plain,
( member(pair(combS,ap_contractE_sk2q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract)
| ~ spl0_12 ),
inference(resolution,[],[f122,f27]) ).
fof(f363,plain,
( $false
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f362,f36]) ).
fof(f364,plain,
~ spl0_12,
inference(avatar_contradiction_clause,[],[f363]) ).
fof(f366,plain,
( combS = comb_app(comb_app(combS,ap_contractE_sk1p(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),ap_contractE_sk1q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)))
| ~ spl0_13 ),
inference(resolution,[],[f126,f26]) ).
fof(f367,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f366,f3]) ).
fof(f368,plain,
~ spl0_13,
inference(avatar_contradiction_clause,[],[f367]) ).
fof(f370,plain,
( comb_app(combS,combK) = comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r))
| ~ spl0_4 ),
inference(resolution,[],[f60,f26]) ).
fof(f435,plain,
( ! [X0,X1] :
( comb_app(X0,X1) != comb_app(combS,combK)
| comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)) = X0 )
| ~ spl0_4 ),
inference(superposition,[],[f4,f370]) ).
fof(f543,plain,
( combS = comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r))
| ~ spl0_4 ),
inference(equality_resolution,[],[f435]) ).
fof(f544,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f543,f3]) ).
fof(f545,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f544]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f61]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f66]) ).
cnf(s9,plain,
~ spl0_1,
inference(sat_conversion,[],[f162]) ).
cnf(s31,plain,
( ~ spl0_3
| spl0_11
| spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f352]) ).
cnf(s32,plain,
~ spl0_11,
inference(sat_conversion,[],[f360]) ).
cnf(s33,plain,
~ spl0_12,
inference(sat_conversion,[],[f364]) ).
cnf(s34,plain,
~ spl0_13,
inference(sat_conversion,[],[f368]) ).
cnf(s66,plain,
~ spl0_4,
inference(sat_conversion,[],[f545]) ).
cnf(s67,plain,
~ spl0_3,
inference(rat,[],[s31,s34,s33,s32]) ).
cnf(s68,plain,
$false,
inference(rat,[],[s1,s66,s67,s2,s9]) ).
fof(f546,plain,
$false,
inference(avatar_sat_refutation,[],[s68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL090-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.15 % Computer : n012.cluster.edu
% 0.06/0.15 % Model : x86_64 x86_64
% 0.06/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.15 % Memory : 8046.5625MB
% 0.06/0.15 % OS : Linux 6.8.0-71-generic
% 0.06/0.15 % CPULimit : 300
% 0.06/0.15 % WCLimit : 300
% 0.06/0.15 % DateTime : Mon Sep 28 21:34:49 UTC 2026
% 0.06/0.15 % CPUTime :
% 0.06/0.15 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 Running first-order theorem proving
% 0.06/0.18 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
% 3.53/1.06 % (3806869)Input is clausal, will run a generic CNF schedule.
% 3.53/1.06 % (3806874)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=149573235:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.53/1.06 % (3806876)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4170664846:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.53/1.06 % (3806875)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=940150606:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.53/1.06 % (3806877)lrs+10_1_sil=8000:sp=occurrence:random_seed=3095044355:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.53/1.06 % (3806878)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1738083522:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.53/1.06 % (3806879)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2103196658:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.53/1.06 % (3806880)dis-21_1_sil=8000:lcm=predicate:random_seed=1932334376: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)
% 3.53/1.06 % (3806878)Refutation not found, incomplete strategy
% 3.53/1.06 % (3806878)------------------------------
% 3.53/1.06 % (3806878)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.06 % (3806878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.06 % (3806878)CaDiCaL version: 2.1.3
% 3.53/1.06 % (3806878)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.06 % (3806878)Time elapsed: 0.001 s
% 3.53/1.06 % (3806878)Peak memory usage: 88 MB
% 3.53/1.06 % (3806878)Instructions burned: 1 (million)
% 3.53/1.06 % (3806879)First to succeed.
% 3.53/1.06 % (3806879)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3806869"
% 3.53/1.06 % (3806877)Also succeeded, but the first one will report.
% 3.53/1.06 % (3806880)Instruction limit reached!
% 3.53/1.06 % (3806880)------------------------------
% 3.53/1.06 % (3806880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.06 % (3806880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.06 % (3806880)CaDiCaL version: 2.1.3
% 3.53/1.06 % (3806880)Termination reason: Instruction limit
% 3.53/1.06 % (3806880)Termination phase: Saturation
% 3.53/1.06 % (3806880)Time elapsed: 0.052 s
% 3.53/1.06 % (3806880)Peak memory usage: 89 MB
% 3.53/1.06 % (3806880)Instructions burned: 118 (million)
% 3.53/1.06 % (3806890)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=1769733396:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.53/1.06 % (3806890)Refutation not found, incomplete strategy
% 3.53/1.06 % (3806890)------------------------------
% 3.53/1.06 % (3806890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.06 % (3806890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.06 % (3806890)CaDiCaL version: 2.1.3
% 3.53/1.06 % (3806890)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.06 % (3806890)Time elapsed: 0.001 s
% 3.53/1.06 % (3806890)Peak memory usage: 88 MB
% 3.53/1.06 % (3806890)Instructions burned: 1 (million)
% 3.53/1.06 % (3806878)------------------------------
% 3.53/1.06 % (3806878)------------------------------
% 3.53/1.06 % (3806879)Refutation found. Thanks to Tanya!
% 3.53/1.06 % SZS status Unsatisfiable for theBenchmark
% 3.53/1.06 % SZS output start Proof for theBenchmark
% See solution above
% 4.03/1.27 % (3806879)------------------------------
% 4.03/1.27 % (3806879)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.27 % (3806879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.27 % (3806879)CaDiCaL version: 2.1.3
% 4.03/1.27 % (3806879)Termination reason: Refutation
% 4.03/1.27 % (3806879)Time elapsed: 0.016 s
% 4.03/1.27 % (3806879)Peak memory usage: 89 MB
% 4.03/1.27 % (3806879)Instructions burned: 26 (million)
% 4.03/1.27 % (3806879)------------------------------
% 4.03/1.27 % (3806879)------------------------------
% 4.03/1.27 % (3806869)Success in time 0.492 s
% 4.03/1.27 % Vampire exiting
%------------------------------------------------------------------------------