%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV678-1 : 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 : n003.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 01:19:15 PM UTC 2026
% Result : Unsatisfiable 3.52s 1.29s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 10 unt; 2 def)
% Number of atoms : 55 ( 17 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 55 ( 27 ~; 26 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 8 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f520,axiom,
( v_a != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nz_0) ).
fof(f735,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X3,X0),X0)
| ~ c_lessequals(X3,X2,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__diff_0) ).
fof(f736,plain,
! [X2,X3,X0,X1] :
( c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X3,X0),X0)
| ~ class_Ring__and__Field_Ofield(X0)
| ~ c_lessequals(X3,X2,tc_nat)
| c_HOL_Ozero__class_Ozero(X0) = X1 ),
inference(reorient_equations,[],[f735]) ).
fof(f775,axiom,
c_lessequals(v_n,v_m,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f777,negated_conjecture,
class_Ring__and__Field_Ofield(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f779,negated_conjecture,
( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a)
| ~ c_lessequals(v_n,v_m,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f825,definition,
( spl0_1
<=> c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) = c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f826,plain,
( c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a)
| spl0_1 ),
inference(avatar_component_clause,[],[f825]) ).
fof(f831,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a),
inference(forward_subsumption_resolution,[],[f779,f775]) ).
fof(f832,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f831,f825]) ).
fof(f834,plain,
( c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) != c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a)
| ~ class_Ring__and__Field_Ofield(t_a)
| ~ c_lessequals(v_n,v_m,tc_nat)
| v_a = c_HOL_Ozero__class_Ozero(t_a)
| spl0_1 ),
inference(superposition,[],[f826,f736]) ).
fof(f835,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| ~ c_lessequals(v_n,v_m,tc_nat)
| v_a = c_HOL_Ozero__class_Ozero(t_a)
| spl0_1 ),
inference(trivial_inequality_removal,[],[f834]) ).
fof(f836,plain,
( ~ c_lessequals(v_n,v_m,tc_nat)
| v_a = c_HOL_Ozero__class_Ozero(t_a)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f835,f777]) ).
fof(f838,plain,
( v_a = c_HOL_Ozero__class_Ozero(t_a)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f836,f775]) ).
fof(f840,definition,
( spl0_3
<=> v_a = c_HOL_Ozero__class_Ozero(t_a) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f841,plain,
( v_a = c_HOL_Ozero__class_Ozero(t_a)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f840]) ).
fof(f849,plain,
( spl0_3
| spl0_1 ),
inference(avatar_split_clause,[],[f838,f825,f840]) ).
fof(f850,plain,
( v_a != v_a
| ~ class_Ring__and__Field_Ofield(t_a)
| ~ spl0_3 ),
inference(superposition,[],[f520,f841]) ).
fof(f854,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f850]) ).
fof(f858,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f854,f777]) ).
fof(f859,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f858]) ).
cnf(s2,plain,
~ spl0_1,
inference(sat_conversion,[],[f832]) ).
cnf(s4,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f849]) ).
cnf(s6,plain,
~ spl0_3,
inference(sat_conversion,[],[f859]) ).
cnf(s7,plain,
spl0_1,
inference(rat,[],[s4,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s2,s7]) ).
fof(f860,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV678-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n003.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 12:15:27 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.52/1.29 % (1548369)Input is clausal, will run a generic CNF schedule.
% 3.52/1.29 % (1548378)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=902584077:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.52/1.29 % (1548379)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=771717418:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.52/1.29 % (1548380)dis-21_1_sil=8000:lcm=predicate:random_seed=2766968616: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)
% 3.52/1.29 % (1548375)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3924012600:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.52/1.29 % (1548376)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3920506890:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.52/1.29 % (1548377)lrs+10_1_sil=8000:sp=occurrence:random_seed=455460694:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.52/1.29 % (1548374)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=1746553344:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.52/1.29 % (1548378)Instruction limit reached!
% 3.52/1.29 % (1548378)------------------------------
% 3.52/1.29 % (1548378)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.29 % (1548378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.29 % (1548378)CaDiCaL version: 2.1.3
% 3.52/1.29 % (1548378)Termination reason: Instruction limit
% 3.52/1.29 % (1548378)Termination phase: Saturation
% 3.52/1.29 % (1548378)Time elapsed: 0.041 s
% 3.52/1.29 % (1548378)Peak memory usage: 89 MB
% 3.52/1.29 % (1548378)Instructions burned: 117 (million)
% 3.52/1.29 % (1548377)Instruction limit reached!
% 3.52/1.29 % (1548377)------------------------------
% 3.52/1.29 % (1548377)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.29 % (1548377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.29 % (1548377)CaDiCaL version: 2.1.3
% 3.52/1.29 % (1548377)Termination reason: Instruction limit
% 3.52/1.29 % (1548377)Termination phase: Saturation
% 3.52/1.29 % (1548377)Time elapsed: 0.069 s
% 3.52/1.29 % (1548377)Peak memory usage: 89 MB
% 3.52/1.29 % (1548377)Instructions burned: 107 (million)
% 3.52/1.29 % (1548380)Instruction limit reached!
% 3.52/1.29 % (1548380)------------------------------
% 3.52/1.29 % (1548380)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.29 % (1548380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.29 % (1548380)CaDiCaL version: 2.1.3
% 3.52/1.29 % (1548380)Termination reason: Instruction limit
% 3.52/1.29 % (1548380)Termination phase: Saturation
% 3.52/1.29 % (1548380)Time elapsed: 0.070 s
% 3.52/1.29 % (1548380)Peak memory usage: 89 MB
% 3.52/1.29 % (1548380)Instructions burned: 118 (million)
% 3.52/1.29 % (1548388)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=3992959900:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.52/1.29 % (1548388)First to succeed.
% 3.52/1.29 % (1548388)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1548369"
% 3.52/1.29 % (1548379)Instruction limit reached!
% 3.52/1.29 % (1548379)------------------------------
% 3.52/1.29 % (1548379)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.29 % (1548379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.29 % (1548379)CaDiCaL version: 2.1.3
% 3.52/1.29 % (1548379)Termination reason: Instruction limit
% 3.52/1.29 % (1548379)Termination phase: Saturation
% 3.52/1.29 % (1548379)Time elapsed: 0.118 s
% 3.52/1.29 % (1548379)Peak memory usage: 90 MB
% 3.52/1.29 % (1548379)Instructions burned: 181 (million)
% 3.52/1.29 % (1548390)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2788159523:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.52/1.29 % (1548389)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2251380140: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)
% 3.52/1.29 % (1548390)Also succeeded, but the first one will report.
% 3.52/1.29 % (1548389)Also succeeded, but the first one will report.
% 3.52/1.29 % (1548388)Refutation found. Thanks to Tanya!
% 3.52/1.29 % SZS status Unsatisfiable for theBenchmark
% 3.52/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.52/1.29 % (1548388)------------------------------
% 3.52/1.29 % (1548388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.29 % (1548388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.29 % (1548388)CaDiCaL version: 2.1.3
% 3.52/1.29 % (1548388)Termination reason: Refutation
% 3.52/1.29 % (1548388)Time elapsed: 0.004 s
% 3.52/1.29 % (1548388)Peak memory usage: 90 MB
% 3.52/1.29 % (1548388)Instructions burned: 9 (million)
% 3.52/1.29 % (1548388)------------------------------
% 3.52/1.29 % (1548388)------------------------------
% 3.52/1.29 % (1548369)Success in time 0.431 s
% 3.52/1.29 % Vampire exiting
%------------------------------------------------------------------------------