%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV580-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:19:01 PM UTC 2026
% Result : Unsatisfiable 3.59s 1.17s
% Output : Refutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 14 unt; 2 def)
% Number of atoms : 57 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 33 ~; 23 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 15 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f232,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,tc_nat),tc_nat,X0) = c_HOL_Oplus__class_Oplus(hAPP(X1,X2),c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X2),X3,tc_nat),tc_nat,X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__head__upt__Suc_0) ).
fof(f591,axiom,
c_HOL_Oord__class_Oless(v_m,v_n,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less_0) ).
fof(f594,axiom,
! [X0,X1] : c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X0),X1,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(X0,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastSucLessThan__greaterThanLessThan_0) ).
fof(f600,axiom,
! [X0] : c_SetInterval_Oord__class_OatLeastLessThan(X0,c_Suc(X0),tc_nat) = c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__singleton_0) ).
fof(f601,plain,
! [X0] : c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(X0,c_Suc(X0),tc_nat),
inference(reorient_equations,[],[f600]) ).
fof(f604,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(t_a)
| c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a),t_a) = c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_calculation_0) ).
fof(f652,axiom,
! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
fof(f662,negated_conjecture,
class_OrderedGroup_Ocomm__monoid__add(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f663,negated_conjecture,
c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f713,definition,
( spl0_1
<=> c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a),t_a) = c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f715,plain,
( c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a),t_a) = c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f713]) ).
fof(f717,definition,
( spl0_2
<=> class_OrderedGroup_Ocomm__monoid__add(t_a) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f718,plain,
( class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f717]) ).
fof(f720,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f604,f717,f713]) ).
fof(f735,plain,
spl0_2,
inference(avatar_split_clause,[],[f662,f717]) ).
fof(f947,plain,
c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a) != c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a),
inference(superposition,[],[f663,f652]) ).
fof(f949,plain,
c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a) != c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(v_m,c_Suc(v_m),tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a),
inference(forward_demodulation,[],[f947,f601]) ).
fof(f1724,plain,
! [X2,X3,X0,X1] :
( c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,tc_nat),tc_nat,X0) = c_HOL_Oplus__class_Oplus(hAPP(X1,X2),c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,tc_nat),tc_nat,X0),X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat) ),
inference(forward_demodulation,[],[f232,f594]) ).
fof(f1737,plain,
( c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a),t_a) = c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f715,f652]) ).
fof(f1738,plain,
( c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a),t_a) = c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(v_m,c_Suc(v_m),tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1737,f601]) ).
fof(f1749,plain,
( c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a),t_a) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a)
| ~ spl0_1 ),
inference(superposition,[],[f949,f1738]) ).
fof(f1750,plain,
( c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ c_HOL_Oord__class_Oless(v_m,v_n,tc_nat)
| ~ spl0_1 ),
inference(superposition,[],[f1749,f1724]) ).
fof(f1751,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ c_HOL_Oord__class_Oless(v_m,v_n,tc_nat)
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f1750]) ).
fof(f1752,plain,
( ~ c_HOL_Oord__class_Oless(v_m,v_n,tc_nat)
| ~ spl0_1
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1751,f718]) ).
fof(f1753,plain,
( $false
| ~ spl0_1
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1752,f591]) ).
fof(f1754,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f1753]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f720]) ).
cnf(s4,plain,
spl0_2,
inference(sat_conversion,[],[f735]) ).
cnf(s51,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f1754]) ).
cnf(s53,plain,
~ spl0_1,
inference(rat,[],[s51,s4]) ).
cnf(s54,plain,
$false,
inference(rat,[],[s1,s4,s53]) ).
fof(f1755,plain,
$false,
inference(avatar_sat_refutation,[],[s54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV580-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n015.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 11:59:02 UTC 2026
% 0.09/0.20 % 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
% 3.59/1.17 % (2576852)Input is clausal, will run a generic CNF schedule.
% 3.59/1.17 % (2576859)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=710379461:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.59/1.17 % (2576857)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=4091604251:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.59/1.17 % (2576861)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3789945369:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.59/1.17 % (2576862)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1435984162:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.59/1.17 % (2576863)dis-21_1_sil=8000:lcm=predicate:random_seed=119922620: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)
% 3.59/1.17 % (2576860)lrs+10_1_sil=8000:sp=occurrence:random_seed=709069094:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.59/1.17 % (2576858)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2966786009:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.59/1.17 % (2576862)First to succeed.
% 3.59/1.17 % (2576862)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2576852"
% 3.59/1.17 % (2576860)Instruction limit reached!
% 3.59/1.17 % (2576860)------------------------------
% 3.59/1.17 % (2576860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.17 % (2576860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.17 % (2576860)CaDiCaL version: 2.1.3
% 3.59/1.17 % (2576860)Termination reason: Instruction limit
% 3.59/1.17 % (2576860)Termination phase: Saturation
% 3.59/1.17 % (2576860)Time elapsed: 0.069 s
% 3.59/1.17 % (2576860)Peak memory usage: 89 MB
% 3.59/1.17 % (2576860)Instructions burned: 107 (million)
% 3.59/1.17 % (2576863)Instruction limit reached!
% 3.59/1.17 % (2576863)------------------------------
% 3.59/1.17 % (2576863)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.17 % (2576863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.17 % (2576863)CaDiCaL version: 2.1.3
% 3.59/1.17 % (2576863)Termination reason: Instruction limit
% 3.59/1.17 % (2576863)Termination phase: Saturation
% 3.59/1.17 % (2576863)Time elapsed: 0.071 s
% 3.59/1.17 % (2576863)Peak memory usage: 89 MB
% 3.59/1.17 % (2576863)Instructions burned: 117 (million)
% 3.59/1.17 % (2576861)Instruction limit reached!
% 3.59/1.17 % (2576861)------------------------------
% 3.59/1.17 % (2576861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.17 % (2576861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.17 % (2576861)CaDiCaL version: 2.1.3
% 3.59/1.17 % (2576861)Termination reason: Instruction limit
% 3.59/1.17 % (2576861)Termination phase: Saturation
% 3.59/1.17 % (2576861)Time elapsed: 0.073 s
% 3.59/1.17 % (2576861)Peak memory usage: 88 MB
% 3.59/1.17 % (2576861)Instructions burned: 115 (million)
% 3.59/1.17 % (2576871)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=3868108217:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.59/1.17 % (2576873)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3949467918:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.59/1.17 % (2576872)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2895564550: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)
% 3.59/1.17 % (2576872)Also succeeded, but the first one will report.
% 3.59/1.17 % (2576862)Refutation found. Thanks to Tanya!
% 3.59/1.17 % SZS status Unsatisfiable for theBenchmark
% 3.59/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 4.03/1.36 % (2576862)------------------------------
% 4.03/1.36 % (2576862)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.36 % (2576862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.36 % (2576862)CaDiCaL version: 2.1.3
% 4.03/1.36 % (2576862)Termination reason: Refutation
% 4.03/1.36 % (2576862)Time elapsed: 0.048 s
% 4.03/1.36 % (2576862)Peak memory usage: 90 MB
% 4.03/1.36 % (2576862)Instructions burned: 69 (million)
% 4.03/1.36 % (2576862)------------------------------
% 4.03/1.36 % (2576862)------------------------------
% 4.03/1.36 % (2576852)Success in time 0.499 s
% 4.03/1.36 % Vampire exiting
%------------------------------------------------------------------------------