%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV254-1 : 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 01:08:32 PM UTC 2026
% Result : Unsatisfiable 5.60s 1.65s
% Output : Refutation 5.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 43 ( 14 unt; 2 def)
% Number of atoms : 77 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 71 ( 37 ~; 32 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1466,axiom,
! [X0,X1] :
( c_less(X0,c_plus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(X0,X1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_1) ).
fof(f2357,axiom,
! [X0,X1] :
( c_plus(X0,X1,tc_nat) != c_0
| X1 = c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
fof(f2358,plain,
! [X0,X1] :
( c_0 != c_plus(X0,X1,tc_nat)
| c_0 = X1 ),
inference(reorient_equations,[],[f2357]) ).
fof(f2377,axiom,
! [X0,X1] :
( c_plus(c_minus(X1,X0,tc_nat),X0,tc_nat) = X1
| ~ c_lessequals(X0,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).
fof(f2429,axiom,
! [X2,X0,X1] :
( c_less(c_plus(X2,X0,tc_nat),c_plus(X2,X1,tc_nat),tc_nat)
| ~ c_less(X0,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
fof(f2432,axiom,
! [X0,X1] : ~ c_less(c_plus(X0,X1,tc_nat),X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
fof(f2433,axiom,
! [X0] :
( c_less(c_0,X0,tc_nat)
| X0 = c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
fof(f2434,plain,
! [X0] :
( c_less(c_0,X0,tc_nat)
| c_0 = X0 ),
inference(reorient_equations,[],[f2433]) ).
fof(f3116,axiom,
! [X2,X0,X1] :
( c_minus(X0,X1,tc_set(X2)) != c_emptyset
| c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
fof(f3117,plain,
! [X2,X0,X1] :
( c_emptyset != c_minus(X0,X1,tc_set(X2))
| c_lessequals(X0,X1,tc_set(X2)) ),
inference(reorient_equations,[],[f3116]) ).
fof(f3260,axiom,
! [X0,X1] : ~ c_less(X0,c_emptyset,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
fof(f3391,negated_conjecture,
! [X0] : c_lessequals(X0,v_x(X0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3392,negated_conjecture,
! [X0] : v_x(X0) = v_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3393,plain,
! [X0] : c_lessequals(X0,v_nat,tc_nat),
inference(definition_unfolding,[],[f3391,f3392]) ).
fof(f3401,plain,
! [X0] : v_nat = c_plus(c_minus(v_nat,X0,tc_nat),X0,tc_nat),
inference(unit_resulting_resolution,[],[f2377,f3393]) ).
fof(f3428,plain,
! [X0] :
( c_0 != v_nat
| c_0 = X0 ),
inference(superposition,[],[f2358,f3401]) ).
fof(f3438,plain,
! [X0,X1] :
( c_less(v_nat,c_plus(c_minus(v_nat,X0,tc_nat),X1,tc_nat),tc_nat)
| ~ c_less(X0,X1,tc_nat) ),
inference(superposition,[],[f2429,f3401]) ).
fof(f3442,plain,
! [X0] : ~ c_less(v_nat,X0,tc_nat),
inference(superposition,[],[f2432,f3401]) ).
fof(f3473,plain,
! [X0,X1] : ~ c_less(X0,X1,tc_nat),
inference(forward_subsumption_resolution,[],[f3438,f3442]) ).
fof(f3476,definition,
( spl0_6
<=> ! [X0] : c_0 = X0 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f3477,plain,
( ! [X0] : c_0 = X0
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f3476]) ).
fof(f3479,definition,
( spl0_7
<=> c_0 = v_nat ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f3481,plain,
( c_0 != v_nat
| spl0_7 ),
inference(avatar_component_clause,[],[f3479]) ).
fof(f3482,plain,
( spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f3428,f3479,f3476]) ).
fof(f3545,plain,
( c_less(c_0,v_nat,tc_nat)
| spl0_7 ),
inference(unit_resulting_resolution,[],[f2434,f3481]) ).
fof(f3590,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f3545,f3473]) ).
fof(f3591,plain,
spl0_7,
inference(avatar_contradiction_clause,[],[f3590]) ).
fof(f3619,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,X1,c_0)
| c_emptyset != c_minus(X0,X1,tc_set(X2)) )
| ~ spl0_6 ),
inference(backward_demodulation,[],[f3117,f3477]) ).
fof(f3633,plain,
( ! [X0] : ~ c_less(X0,c_emptyset,c_0)
| ~ spl0_6 ),
inference(backward_demodulation,[],[f3260,f3477]) ).
fof(f3728,plain,
( ! [X0,X1] :
( c_less(X0,c_plus(X1,c_1,c_0),c_0)
| ~ c_lessequals(X0,X1,tc_IntDef_Oint) )
| ~ spl0_6 ),
inference(backward_demodulation,[],[f1466,f3477]) ).
fof(f3846,plain,
( ! [X0,X1] :
( c_less(X0,c_0,c_0)
| ~ c_lessequals(X0,X1,tc_IntDef_Oint) )
| ~ spl0_6 ),
inference(forward_demodulation,[],[f3728,f3477]) ).
fof(f3895,plain,
( ! [X0] : ~ c_less(X0,c_0,c_0)
| ~ spl0_6 ),
inference(forward_demodulation,[],[f3633,f3477]) ).
fof(f3909,plain,
( ! [X0,X1] :
( c_0 != c_emptyset
| c_lessequals(X0,X1,c_0) )
| ~ spl0_6 ),
inference(forward_demodulation,[],[f3619,f3477]) ).
fof(f3931,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,X1,c_0)
| c_less(X0,c_0,c_0) )
| ~ spl0_6 ),
inference(forward_demodulation,[],[f3846,f3477]) ).
fof(f3940,plain,
( ! [X0,X1] : c_lessequals(X0,X1,c_0)
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f3909,f3477]) ).
fof(f3962,plain,
( ! [X0,X1] : ~ c_lessequals(X0,X1,c_0)
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f3931,f3895]) ).
fof(f3969,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f3962,f3940]) ).
fof(f3970,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f3969]) ).
cnf(s5,plain,
( spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f3482]) ).
cnf(s11,plain,
spl0_7,
inference(sat_conversion,[],[f3591]) ).
cnf(s26,plain,
~ spl0_6,
inference(sat_conversion,[],[f3970]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s5,s11,s26]) ).
fof(f3972,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV254-1 : 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 : n016.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 10:23:48 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 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
% 4.45/1.46 % (3532646)Input is clausal, will run a generic CNF schedule.
% 4.45/1.46 % (3532667)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=115566519:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.45/1.46 % (3532672)dis-21_1_sil=8000:lcm=predicate:random_seed=2510428808: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)
% 4.45/1.46 % (3532666)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=4025224683:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.45/1.46 % (3532668)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1012314492:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.45/1.46 % (3532671)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=361513600:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.45/1.46 % (3532669)lrs+10_1_sil=8000:sp=occurrence:random_seed=3739921219:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.45/1.46 % (3532670)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1667734524:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.45/1.46 % (3532669)Refutation not found, incomplete strategy
% 4.45/1.46 % (3532669)------------------------------
% 4.45/1.46 % (3532669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.46 % (3532669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.46 % (3532669)CaDiCaL version: 2.1.3
% 4.45/1.46 % (3532669)Termination reason: Refutation not found, incomplete strategy
% 4.45/1.46 % (3532669)Time elapsed: 0.006 s
% 4.45/1.46 % (3532669)Peak memory usage: 90 MB
% 4.45/1.46 % (3532669)Instructions burned: 7 (million)
% 4.45/1.46 % (3532670)Refutation not found, incomplete strategy
% 4.45/1.46 % (3532670)------------------------------
% 4.45/1.46 % (3532670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.46 % (3532670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.46 % (3532670)CaDiCaL version: 2.1.3
% 4.45/1.46 % (3532670)Termination reason: Refutation not found, incomplete strategy
% 4.45/1.46 % (3532670)Time elapsed: 0.008 s
% 4.45/1.46 % (3532670)Peak memory usage: 90 MB
% 4.45/1.46 % (3532670)Instructions burned: 11 (million)
% 4.45/1.46 % (3532672)Instruction limit reached!
% 4.45/1.46 % (3532672)------------------------------
% 4.45/1.46 % (3532672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.46 % (3532672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.46 % (3532672)CaDiCaL version: 2.1.3
% 4.45/1.46 % (3532672)Termination reason: Instruction limit
% 4.45/1.46 % (3532672)Termination phase: Saturation
% 4.45/1.46 % (3532672)Time elapsed: 0.064 s
% 4.45/1.46 % (3532672)Peak memory usage: 90 MB
% 4.45/1.46 % (3532672)Instructions burned: 118 (million)
% 4.45/1.46 % (3532671)Instruction limit reached!
% 4.45/1.46 % (3532671)------------------------------
% 4.45/1.46 % (3532671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.46 % (3532671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.46 % (3532671)CaDiCaL version: 2.1.3
% 4.45/1.46 % (3532671)Termination reason: Instruction limit
% 4.45/1.46 % (3532671)Termination phase: Saturation
% 4.45/1.46 % (3532671)Time elapsed: 0.117 s
% 4.45/1.46 % (3532671)Peak memory usage: 91 MB
% 4.45/1.46 % (3532671)Instructions burned: 181 (million)
% 4.45/1.46 % (3532747)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=646620768:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.45/1.46 % (3532747)Refutation not found, incomplete strategy
% 4.45/1.46 % (3532747)------------------------------
% 4.45/1.46 % (3532747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.46 % (3532747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.46 % (3532747)CaDiCaL version: 2.1.3
% 4.45/1.46 % (3532747)Termination reason: Refutation not found, incomplete strategy
% 4.45/1.46 % (3532747)Time elapsed: 0.006 s
% 4.45/1.46 % (3532747)Peak memory usage: 90 MB
% 4.45/1.46 % (3532747)Instructions burned: 7 (million)
% 4.45/1.46 % (3532769)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=4096335130:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 5.60/1.65 % (3532670)------------------------------
% 5.60/1.65 % (3532670)------------------------------
% 5.60/1.65 % (3532669)------------------------------
% 5.60/1.65 % (3532669)------------------------------
% 5.60/1.65 % (3532769)First to succeed.
% 5.60/1.65 % (3532769)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3532646"
% 5.60/1.65 % (3532790)lrs+10_64_to=lpo:sil=8000:random_seed=3689578703:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 5.60/1.65 % (3532789)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3300363657:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 5.60/1.65 % (3532789)Refutation not found, incomplete strategy
% 5.60/1.65 % (3532789)------------------------------
% 5.60/1.65 % (3532789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.60/1.65 % (3532789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.65 % (3532789)CaDiCaL version: 2.1.3
% 5.60/1.65 % (3532789)Termination reason: Refutation not found, incomplete strategy
% 5.60/1.65 % (3532789)Time elapsed: 0.033 s
% 5.60/1.65 % (3532789)Peak memory usage: 90 MB
% 5.60/1.65 % (3532789)Instructions burned: 55 (million)
% 5.60/1.65 % (3532747)------------------------------
% 5.60/1.65 % (3532747)------------------------------
% 5.60/1.65 % (3532790)Instruction limit reached!
% 5.60/1.65 % (3532790)------------------------------
% 5.60/1.65 % (3532790)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.60/1.65 % (3532790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.65 % (3532790)CaDiCaL version: 2.1.3
% 5.60/1.65 % (3532790)Termination reason: Instruction limit
% 5.60/1.65 % (3532790)Termination phase: Saturation
% 5.60/1.65 % (3532790)Time elapsed: 0.073 s
% 5.60/1.65 % (3532790)Peak memory usage: 91 MB
% 5.60/1.65 % (3532790)Instructions burned: 126 (million)
% 5.60/1.65 % (3532667)Also succeeded, but the first one will report.
% 5.60/1.65 % (3532769)Refutation found. Thanks to Tanya!
% 5.60/1.65 % SZS status Unsatisfiable for theBenchmark
% 5.60/1.65 % SZS output start Proof for theBenchmark
% See solution above
% 5.60/1.65 % (3532769)------------------------------
% 5.60/1.65 % (3532769)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.60/1.65 % (3532769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.60/1.65 % (3532769)CaDiCaL version: 2.1.3
% 5.60/1.65 % (3532769)Termination reason: Refutation
% 5.60/1.65 % (3532769)Time elapsed: 0.035 s
% 5.60/1.65 % (3532769)Peak memory usage: 92 MB
% 5.60/1.65 % (3532769)Instructions burned: 54 (million)
% 5.60/1.65 % (3532769)------------------------------
% 5.60/1.65 % (3532769)------------------------------
% 5.60/1.65 % (3532646)Success in time 0.754 s
% 5.60/1.65 % Vampire exiting
%------------------------------------------------------------------------------