%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV616-1 : 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 : n007.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 01:19:06 PM UTC 2026
% Result : Unsatisfiable 3.89s 1.25s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 9 ( 8 unt; 0 def)
% Number of atoms : 10 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 5 ~; 1 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 9 ( 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f500,axiom,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
fof(f1031,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),X0) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult_0) ).
fof(f1115,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1235,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(f1310,plain,
! [X2,X0,X1] : c_Power_Opower__class_Opower(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),
inference(resolution,[],[f1031,f1235]) ).
fof(f3100,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_k,v_n,tc_nat),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(superposition,[],[f1115,f1310]) ).
fof(f3113,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f3100,f500]) ).
fof(f3125,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f3113,f1310]) ).
fof(f3126,plain,
$false,
inference(trivial_inequality_removal,[],[f3125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV616-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n007.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 12:01:26 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running first-order theorem proving
% 0.08/0.20 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
% 3.89/1.25 % (2346407)Input is clausal, will run a generic CNF schedule.
% 3.89/1.25 % (2346415)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3094126602:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.89/1.25 % (2346418)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=202271694:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.89/1.25 % (2346417)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4228532502:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.89/1.25 % (2346413)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=4137728814:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.89/1.25 % (2346419)dis-21_1_sil=8000:lcm=predicate:random_seed=2768352393: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)
% 3.89/1.25 % (2346414)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1482608897:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.89/1.25 % (2346416)lrs+10_1_sil=8000:sp=occurrence:random_seed=2590507751:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.89/1.25 % (2346419)Instruction limit reached!
% 3.89/1.25 % (2346419)------------------------------
% 3.89/1.25 % (2346419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.25 % (2346419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.25 % (2346419)CaDiCaL version: 2.1.3
% 3.89/1.25 % (2346419)Termination reason: Instruction limit
% 3.89/1.25 % (2346419)Termination phase: Saturation
% 3.89/1.25 % (2346419)Time elapsed: 0.061 s
% 3.89/1.25 % (2346419)Peak memory usage: 89 MB
% 3.89/1.25 % (2346419)Instructions burned: 119 (million)
% 3.89/1.25 % (2346416)Instruction limit reached!
% 3.89/1.25 % (2346416)------------------------------
% 3.89/1.25 % (2346416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.25 % (2346416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.25 % (2346416)CaDiCaL version: 2.1.3
% 3.89/1.25 % (2346416)Termination reason: Instruction limit
% 3.89/1.25 % (2346416)Termination phase: Saturation
% 3.89/1.25 % (2346416)Time elapsed: 0.070 s
% 3.89/1.25 % (2346416)Peak memory usage: 90 MB
% 3.89/1.25 % (2346416)Instructions burned: 108 (million)
% 3.89/1.25 % (2346417)Instruction limit reached!
% 3.89/1.25 % (2346417)------------------------------
% 3.89/1.25 % (2346417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.25 % (2346417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.25 % (2346417)CaDiCaL version: 2.1.3
% 3.89/1.25 % (2346417)Termination reason: Instruction limit
% 3.89/1.25 % (2346417)Termination phase: Saturation
% 3.89/1.25 % (2346417)Time elapsed: 0.072 s
% 3.89/1.25 % (2346417)Peak memory usage: 89 MB
% 3.89/1.25 % (2346417)Instructions burned: 114 (million)
% 3.89/1.25 % (2346418)First to succeed.
% 3.89/1.25 % (2346418)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2346407"
% 3.89/1.25 % (2346427)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=1628951364:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.89/1.25 % (2346427)Refutation not found, incomplete strategy
% 3.89/1.25 % (2346427)------------------------------
% 3.89/1.25 % (2346427)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.25 % (2346427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.25 % (2346427)CaDiCaL version: 2.1.3
% 3.89/1.25 % (2346427)Termination reason: Refutation not found, incomplete strategy
% 3.89/1.25 % (2346427)Time elapsed: 0.008 s
% 3.89/1.25 % (2346427)Peak memory usage: 89 MB
% 3.89/1.25 % (2346427)Instructions burned: 11 (million)
% 3.89/1.25 % (2346428)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2100744368: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)
% 3.89/1.25 % (2346429)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3705863332:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.89/1.25 % (2346428)Instruction limit reached!
% 3.89/1.25 % (2346428)------------------------------
% 3.89/1.25 % (2346428)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.25 % (2346428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.25 % (2346428)CaDiCaL version: 2.1.3
% 3.89/1.25 % (2346428)Termination reason: Instruction limit
% 3.89/1.25 % (2346428)Termination phase: Saturation
% 3.89/1.25 % (2346428)Time elapsed: 0.100 s
% 3.89/1.25 % (2346428)Peak memory usage: 91 MB
% 3.89/1.25 % (2346428)Instructions burned: 190 (million)
% 3.89/1.25 % (2346429)Instruction limit reached!
% 3.89/1.25 % (2346429)------------------------------
% 3.89/1.25 % (2346429)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.25 % (2346429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.25 % (2346429)CaDiCaL version: 2.1.3
% 3.89/1.25 % (2346429)Termination reason: Instruction limit
% 3.89/1.25 % (2346429)Termination phase: Saturation
% 3.89/1.25 % (2346429)Time elapsed: 0.116 s
% 3.89/1.25 % (2346429)Peak memory usage: 91 MB
% 3.89/1.25 % (2346429)Instructions burned: 219 (million)
% 3.89/1.25 % (2346418)Refutation found. Thanks to Tanya!
% 3.89/1.25 % SZS status Unsatisfiable for theBenchmark
% 3.89/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.89/1.25 % (2346418)------------------------------
% 3.89/1.25 % (2346418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.89/1.25 % (2346418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.89/1.25 % (2346418)CaDiCaL version: 2.1.3
% 3.89/1.25 % (2346418)Termination reason: Refutation
% 3.89/1.25 % (2346418)Time elapsed: 0.079 s
% 3.89/1.25 % (2346418)Peak memory usage: 90 MB
% 3.89/1.25 % (2346418)Instructions burned: 116 (million)
% 3.89/1.25 % (2346418)------------------------------
% 3.89/1.25 % (2346418)------------------------------
% 3.89/1.25 % (2346407)Success in time 0.511 s
% 3.89/1.25 % Vampire exiting
%------------------------------------------------------------------------------