%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV634-1 : 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 : n019.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 01:19:09 PM UTC 2026
% Result : Unsatisfiable 4.87s 1.28s
% Output : Refutation 4.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 8 ( 6 unt; 0 def)
% Number of atoms : 10 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 4 ( 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f568,axiom,
! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
fof(f1353,axiom,
! [X2,X0,X1] :
( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),X2,tc_Complex_Ocomplex)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__cancel_0) ).
fof(f1510,axiom,
c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__arith_I115_J_0) ).
fof(f1643,negated_conjecture,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1776,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f1643,f1510]) ).
fof(f1784,plain,
( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
inference(superposition,[],[f1776,f1353]) ).
fof(f1785,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat),
inference(trivial_inequality_removal,[],[f1784]) ).
fof(f1786,plain,
$false,
inference(forward_subsumption_resolution,[],[f1785,f568]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV634-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 12:07:04 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
% 4.87/1.27 % (3959000)Input is clausal, will run a generic CNF schedule.
% 4.87/1.27 % (3959010)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4069877337:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.87/1.27 % (3959005)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=4025174313:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.87/1.27 % (3959011)dis-21_1_sil=8000:lcm=predicate:random_seed=555937890: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)
% 4.87/1.27 % (3959008)lrs+10_1_sil=8000:sp=occurrence:random_seed=863698091:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.87/1.27 % (3959009)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3485671471:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.87/1.27 % (3959006)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3003696469:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.87/1.27 % (3959007)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3716242920:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.87/1.27 % (3959010)Instruction limit reached!
% 4.87/1.27 % (3959010)------------------------------
% 4.87/1.27 % (3959010)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.87/1.27 % (3959010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.87/1.27 % (3959010)CaDiCaL version: 2.1.3
% 4.87/1.27 % (3959010)Termination reason: Instruction limit
% 4.87/1.27 % (3959010)Termination phase: Saturation
% 4.87/1.27 % (3959010)Time elapsed: 0.062 s
% 4.87/1.27 % (3959010)Peak memory usage: 90 MB
% 4.87/1.27 % (3959010)Instructions burned: 180 (million)
% 4.87/1.27 % (3959011)Instruction limit reached!
% 4.87/1.27 % (3959011)------------------------------
% 4.87/1.27 % (3959011)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.87/1.27 % (3959011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.87/1.27 % (3959011)CaDiCaL version: 2.1.3
% 4.87/1.27 % (3959011)Termination reason: Instruction limit
% 4.87/1.27 % (3959011)Termination phase: Saturation
% 4.87/1.27 % (3959011)Time elapsed: 0.065 s
% 4.87/1.27 % (3959011)Peak memory usage: 90 MB
% 4.87/1.27 % (3959011)Instructions burned: 118 (million)
% 4.87/1.27 % (3959008)Instruction limit reached!
% 4.87/1.27 % (3959008)------------------------------
% 4.87/1.27 % (3959008)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.87/1.27 % (3959008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.87/1.27 % (3959008)CaDiCaL version: 2.1.3
% 4.87/1.27 % (3959008)Termination reason: Instruction limit
% 4.87/1.27 % (3959008)Termination phase: Saturation
% 4.87/1.27 % (3959008)Time elapsed: 0.069 s
% 4.87/1.27 % (3959008)Peak memory usage: 89 MB
% 4.87/1.27 % (3959008)Instructions burned: 108 (million)
% 4.87/1.27 % (3959009)Instruction limit reached!
% 4.87/1.27 % (3959009)------------------------------
% 4.87/1.27 % (3959009)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.87/1.27 % (3959009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.87/1.28 % (3959009)CaDiCaL version: 2.1.3
% 4.87/1.28 % (3959009)Termination reason: Instruction limit
% 4.87/1.28 % (3959009)Termination phase: Saturation
% 4.87/1.28 % (3959009)Time elapsed: 0.074 s
% 4.87/1.28 % (3959009)Peak memory usage: 90 MB
% 4.87/1.28 % (3959009)Instructions burned: 114 (million)
% 4.87/1.28 % (3959019)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=1241237248:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.87/1.28 % (3959019)Refutation not found, incomplete strategy
% 4.87/1.28 % (3959019)------------------------------
% 4.87/1.28 % (3959019)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.87/1.28 % (3959019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.87/1.28 % (3959019)CaDiCaL version: 2.1.3
% 4.87/1.28 % (3959019)Termination reason: Refutation not found, incomplete strategy
% 4.87/1.28 % (3959019)Time elapsed: 0.008 s
% 4.87/1.28 % (3959019)Peak memory usage: 89 MB
% 4.87/1.28 % (3959019)Instructions burned: 21 (million)
% 4.87/1.28 % (3959020)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2588948580: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)
% 4.87/1.28 % (3959021)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=4174061861:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.87/1.28 % (3959022)lrs+10_64_to=lpo:sil=8000:random_seed=4159395900:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 4.87/1.28 % (3959021)First to succeed.
% 4.87/1.28 % (3959021)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3959000"
% 4.87/1.28 % (3959020)Instruction limit reached!
% 4.87/1.28 % (3959020)------------------------------
% 4.87/1.28 % (3959020)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.87/1.28 % (3959020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.87/1.28 % (3959020)CaDiCaL version: 2.1.3
% 4.87/1.28 % (3959020)Termination reason: Instruction limit
% 4.87/1.28 % (3959020)Termination phase: Saturation
% 4.87/1.28 % (3959020)Time elapsed: 0.094 s
% 4.87/1.28 % (3959020)Peak memory usage: 91 MB
% 4.87/1.28 % (3959020)Instructions burned: 191 (million)
% 4.87/1.28 % (3959022)Instruction limit reached!
% 4.87/1.28 % (3959022)------------------------------
% 4.87/1.28 % (3959022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.87/1.28 % (3959022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.87/1.28 % (3959022)CaDiCaL version: 2.1.3
% 4.87/1.28 % (3959022)Termination reason: Instruction limit
% 4.87/1.28 % (3959022)Termination phase: Saturation
% 4.87/1.28 % (3959022)Time elapsed: 0.078 s
% 4.87/1.28 % (3959022)Peak memory usage: 90 MB
% 4.87/1.28 % (3959022)Instructions burned: 126 (million)
% 4.87/1.28 % (3959019)------------------------------
% 4.87/1.28 % (3959019)------------------------------
% 4.87/1.28 % (3959027)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=872422763:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 4.87/1.28 % (3959029)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=2543139191:i=3394:sd=4:ss=included:sgt=64_2995 on theBenchmark for (2995ds/3394Mi)
% 4.87/1.28 % (3959028)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=875531130:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 4.87/1.28 % (3959021)Refutation found. Thanks to Tanya!
% 4.87/1.28 % SZS status Unsatisfiable for theBenchmark
% 4.87/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 4.87/1.28 % (3959021)------------------------------
% 4.87/1.28 % (3959021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.87/1.28 % (3959021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.87/1.28 % (3959021)CaDiCaL version: 2.1.3
% 4.87/1.28 % (3959021)Termination reason: Refutation
% 4.87/1.28 % (3959021)Time elapsed: 0.031 s
% 4.87/1.28 % (3959021)Peak memory usage: 90 MB
% 4.87/1.28 % (3959021)Instructions burned: 53 (million)
% 4.87/1.28 % (3959021)------------------------------
% 4.87/1.28 % (3959021)------------------------------
% 4.87/1.28 % (3959000)Success in time 0.652 s
% 4.87/1.28 % Vampire exiting
%------------------------------------------------------------------------------