%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV578-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 5.68s 1.64s
% Output : Refutation 5.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 10 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 8 ( 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1277,axiom,
! [X2,X3,X0,X1] :
( c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,tc_nat),tc_nat,X0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),hAPP(X1,X2)),c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,X2),X3,tc_nat),tc_nat,X0))
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__head__upt__Suc_0) ).
fof(f1281,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less_0) ).
fof(f1282,axiom,
! [X0,X1] : c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,X0),X1,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(X0,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastSucLessThan__greaterThanLessThan_0) ).
fof(f1283,plain,
! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanLessThan(X0,X1,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,X0),X1,tc_nat),
inference(reorient_equations,[],[f1282]) ).
fof(f1307,negated_conjecture,
class_OrderedGroup_Ocomm__monoid__add(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f1308,negated_conjecture,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),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)) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1433,plain,
c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(v_f,v_m)),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,v_m),v_n,tc_nat),tc_nat,t_a)),
inference(forward_demodulation,[],[f1308,f1283]) ).
fof(f1441,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)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n)) ),
inference(superposition,[],[f1433,f1277]) ).
fof(f1442,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(t_a)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n)) ),
inference(trivial_inequality_removal,[],[f1441]) ).
fof(f1443,plain,
~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_m,tc_nat),v_n)),
inference(forward_subsumption_resolution,[],[f1442,f1307]) ).
fof(f1460,plain,
$false,
inference(forward_subsumption_resolution,[],[f1443,f1281]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV578-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n013.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 11:54:51 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running first-order theorem proving
% 0.10/0.23 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
% 5.68/1.64 % (1127688)Input is clausal, will run a generic CNF schedule.
% 5.68/1.64 % (1127696)lrs+10_1_sil=8000:sp=occurrence:random_seed=701631173:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.68/1.64 % (1127696)Instruction limit reached!
% 5.68/1.64 % (1127696)------------------------------
% 5.68/1.64 % (1127696)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.64 % (1127696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.64 % (1127696)CaDiCaL version: 2.1.3
% 5.68/1.64 % (1127696)Termination reason: Instruction limit
% 5.68/1.64 % (1127696)Termination phase: Saturation
% 5.68/1.64 % (1127696)Time elapsed: 0.036 s
% 5.68/1.64 % (1127696)Peak memory usage: 89 MB
% 5.68/1.64 % (1127696)Instructions burned: 108 (million)
% 5.68/1.64 % (1127699)dis-21_1_sil=8000:lcm=predicate:random_seed=1287060299: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)
% 5.68/1.64 % (1127698)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2599511039:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.68/1.64 % (1127694)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=411136423:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.68/1.64 % (1127695)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2862186983:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.68/1.64 % (1127693)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=2483974941:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.68/1.64 % (1127697)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=109140719:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.68/1.64 % (1127699)Instruction limit reached!
% 5.68/1.64 % (1127699)------------------------------
% 5.68/1.64 % (1127699)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.64 % (1127699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.64 % (1127699)CaDiCaL version: 2.1.3
% 5.68/1.64 % (1127699)Termination reason: Instruction limit
% 5.68/1.64 % (1127699)Termination phase: Saturation
% 5.68/1.64 % (1127699)Time elapsed: 0.069 s
% 5.68/1.64 % (1127699)Peak memory usage: 90 MB
% 5.68/1.64 % (1127699)Instructions burned: 118 (million)
% 5.68/1.64 % (1127697)Instruction limit reached!
% 5.68/1.64 % (1127697)------------------------------
% 5.68/1.64 % (1127697)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.64 % (1127697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.64 % (1127697)CaDiCaL version: 2.1.3
% 5.68/1.64 % (1127697)Termination reason: Instruction limit
% 5.68/1.64 % (1127697)Termination phase: Saturation
% 5.68/1.64 % (1127697)Time elapsed: 0.073 s
% 5.68/1.64 % (1127697)Peak memory usage: 89 MB
% 5.68/1.64 % (1127697)Instructions burned: 115 (million)
% 5.68/1.64 % (1127698)Instruction limit reached!
% 5.68/1.64 % (1127698)------------------------------
% 5.68/1.64 % (1127698)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.64 % (1127698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.64 % (1127698)CaDiCaL version: 2.1.3
% 5.68/1.64 % (1127698)Termination reason: Instruction limit
% 5.68/1.64 % (1127698)Termination phase: Saturation
% 5.68/1.64 % (1127698)Time elapsed: 0.105 s
% 5.68/1.64 % (1127698)Peak memory usage: 90 MB
% 5.68/1.64 % (1127698)Instructions burned: 181 (million)
% 5.68/1.64 % (1127701)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=3949233032:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.68/1.64 % (1127701)Refutation not found, incomplete strategy
% 5.68/1.64 % (1127701)------------------------------
% 5.68/1.64 % (1127701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.64 % (1127701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.64 % (1127701)CaDiCaL version: 2.1.3
% 5.68/1.64 % (1127701)Termination reason: Refutation not found, incomplete strategy
% 5.68/1.64 % (1127701)Time elapsed: 0.013 s
% 5.68/1.64 % (1127701)Peak memory usage: 89 MB
% 5.68/1.64 % (1127701)Instructions burned: 39 (million)
% 5.68/1.64 % (1127708)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2108699929: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)
% 5.68/1.64 % (1127709)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2892907787:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 5.68/1.64 % (1127709)First to succeed.
% 5.68/1.64 % (1127710)lrs+10_64_to=lpo:sil=8000:random_seed=4259693852:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 5.68/1.64 % (1127709)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1127688"
% 5.68/1.64 % (1127708)Also succeeded, but the first one will report.
% 5.68/1.64 % (1127701)------------------------------
% 5.68/1.64 % (1127701)------------------------------
% 5.68/1.64 % (1127710)Instruction limit reached!
% 5.68/1.64 % (1127710)------------------------------
% 5.68/1.64 % (1127710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.64 % (1127710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.64 % (1127710)CaDiCaL version: 2.1.3
% 5.68/1.64 % (1127710)Termination reason: Instruction limit
% 5.68/1.64 % (1127710)Termination phase: Saturation
% 5.68/1.64 % (1127710)Time elapsed: 0.080 s
% 5.68/1.64 % (1127710)Peak memory usage: 90 MB
% 5.68/1.64 % (1127710)Instructions burned: 126 (million)
% 5.68/1.64 % (1127715)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3390025860:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 5.68/1.64 % (1127715)Instruction limit reached!
% 5.68/1.64 % (1127715)------------------------------
% 5.68/1.64 % (1127715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.64 % (1127715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.64 % (1127715)CaDiCaL version: 2.1.3
% 5.68/1.64 % (1127715)Termination reason: Instruction limit
% 5.68/1.64 % (1127715)Termination phase: Saturation
% 5.68/1.64 % (1127715)Time elapsed: 0.065 s
% 5.68/1.64 % (1127715)Peak memory usage: 91 MB
% 5.68/1.64 % (1127715)Instructions burned: 197 (million)
% 5.68/1.64 % (1127716)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=4009222724:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 5.68/1.64 % (1127709)Refutation found. Thanks to Tanya!
% 5.68/1.64 % SZS status Unsatisfiable for theBenchmark
% 5.68/1.64 % SZS output start Proof for theBenchmark
% See solution above
% 5.68/1.64 % (1127709)------------------------------
% 5.68/1.64 % (1127709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.64 % (1127709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.64 % (1127709)CaDiCaL version: 2.1.3
% 5.68/1.64 % (1127709)Termination reason: Refutation
% 5.68/1.64 % (1127709)Time elapsed: 0.031 s
% 5.68/1.64 % (1127709)Peak memory usage: 89 MB
% 5.68/1.64 % (1127709)Instructions burned: 54 (million)
% 5.68/1.64 % (1127709)------------------------------
% 5.68/1.64 % (1127709)------------------------------
% 5.68/1.64 % (1127688)Success in time 0.765 s
% 5.68/1.64 % Vampire exiting
%------------------------------------------------------------------------------