%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV632-1 : 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 : n017.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 01:19:08 PM UTC 2026
% Result : Unsatisfiable 5.89s 1.69s
% Output : Refutation 5.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 8 unt; 0 def)
% Number of atoms : 16 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 10 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 8 ( 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f626,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(f1429,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(f1590,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(f1691,axiom,
! [X2,X3,X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f1723,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(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),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(f1737,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1856,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(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f1723,f1590]) ).
fof(f1865,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)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
inference(superposition,[],[f1856,f1691]) ).
fof(f1866,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_subsumption_resolution,[],[f1865,f1737]) ).
fof(f1907,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,[],[f1866,f1429]) ).
fof(f1908,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,[],[f1907]) ).
fof(f1909,plain,
$false,
inference(forward_subsumption_resolution,[],[f1908,f626]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV632-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 % Computer : n017.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Mon Sep 28 12:02:09 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 Running first-order theorem proving
% 0.11/0.24 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
% 5.89/1.69 % (3499438)Input is clausal, will run a generic CNF schedule.
% 5.89/1.69 % (3499579)dis-21_1_sil=8000:lcm=predicate:random_seed=2214932428: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)
% 5.89/1.69 % (3499574)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=291859165:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.89/1.69 % (3499576)lrs+10_1_sil=8000:sp=occurrence:random_seed=4057860482:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.89/1.69 % (3499573)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=2504055362:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.89/1.69 % (3499577)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1654678494:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.89/1.69 % (3499575)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1634467532:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.89/1.69 % (3499578)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3408982515:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.89/1.69 % (3499579)Instruction limit reached!
% 5.89/1.69 % (3499579)------------------------------
% 5.89/1.69 % (3499579)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.89/1.69 % (3499579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.89/1.69 % (3499579)CaDiCaL version: 2.1.3
% 5.89/1.69 % (3499579)Termination reason: Instruction limit
% 5.89/1.69 % (3499579)Termination phase: Saturation
% 5.89/1.69 % (3499579)Time elapsed: 0.035 s
% 5.89/1.69 % (3499579)Peak memory usage: 90 MB
% 5.89/1.69 % (3499579)Instructions burned: 118 (million)
% 5.89/1.69 % (3499576)Instruction limit reached!
% 5.89/1.69 % (3499576)------------------------------
% 5.89/1.69 % (3499576)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.89/1.69 % (3499576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.89/1.69 % (3499576)CaDiCaL version: 2.1.3
% 5.89/1.69 % (3499576)Termination reason: Instruction limit
% 5.89/1.69 % (3499576)Termination phase: Saturation
% 5.89/1.69 % (3499576)Time elapsed: 0.070 s
% 5.89/1.69 % (3499576)Peak memory usage: 90 MB
% 5.89/1.69 % (3499576)Instructions burned: 108 (million)
% 5.89/1.69 % (3499577)Instruction limit reached!
% 5.89/1.69 % (3499577)------------------------------
% 5.89/1.69 % (3499577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.89/1.69 % (3499577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.89/1.69 % (3499577)CaDiCaL version: 2.1.3
% 5.89/1.69 % (3499577)Termination reason: Instruction limit
% 5.89/1.69 % (3499577)Termination phase: Saturation
% 5.89/1.69 % (3499577)Time elapsed: 0.073 s
% 5.89/1.69 % (3499577)Peak memory usage: 90 MB
% 5.89/1.69 % (3499577)Instructions burned: 115 (million)
% 5.89/1.69 % (3499578)Instruction limit reached!
% 5.89/1.69 % (3499578)------------------------------
% 5.89/1.69 % (3499578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.89/1.69 % (3499578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.89/1.69 % (3499578)CaDiCaL version: 2.1.3
% 5.89/1.69 % (3499578)Termination reason: Instruction limit
% 5.89/1.69 % (3499578)Termination phase: Saturation
% 5.89/1.69 % (3499578)Time elapsed: 0.117 s
% 5.89/1.69 % (3499578)Peak memory usage: 90 MB
% 5.89/1.69 % (3499578)Instructions burned: 180 (million)
% 5.89/1.69 % (3499587)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=2637705883:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.89/1.69 % (3499587)Refutation not found, incomplete strategy
% 5.89/1.69 % (3499587)------------------------------
% 5.89/1.69 % (3499587)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.89/1.69 % (3499587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.89/1.69 % (3499587)CaDiCaL version: 2.1.3
% 5.89/1.69 % (3499587)Termination reason: Refutation not found, incomplete strategy
% 5.89/1.69 % (3499587)Time elapsed: 0.008 s
% 5.89/1.69 % (3499587)Peak memory usage: 89 MB
% 5.89/1.69 % (3499587)Instructions burned: 21 (million)
% 5.89/1.69 % (3499588)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=640833010: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)
% 5.89/1.69 % (3499589)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3084330143:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.89/1.69 % (3499589)First to succeed.
% 5.89/1.69 % (3499589)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3499438"
% 5.89/1.69 % (3499590)lrs+10_64_to=lpo:sil=8000:random_seed=2232006535:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 5.89/1.69 % (3499587)------------------------------
% 5.89/1.69 % (3499587)------------------------------
% 5.89/1.69 % (3499588)Instruction limit reached!
% 5.89/1.69 % (3499588)------------------------------
% 5.89/1.69 % (3499588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.89/1.69 % (3499588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.89/1.69 % (3499588)CaDiCaL version: 2.1.3
% 5.89/1.69 % (3499588)Termination reason: Instruction limit
% 5.89/1.69 % (3499588)Termination phase: Saturation
% 5.89/1.69 % (3499588)Time elapsed: 0.097 s
% 5.89/1.69 % (3499588)Peak memory usage: 91 MB
% 5.89/1.69 % (3499588)Instructions burned: 190 (million)
% 5.89/1.69 % (3499590)Instruction limit reached!
% 5.89/1.69 % (3499590)------------------------------
% 5.89/1.69 % (3499590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.89/1.69 % (3499590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.89/1.69 % (3499590)CaDiCaL version: 2.1.3
% 5.89/1.69 % (3499590)Termination reason: Instruction limit
% 5.89/1.69 % (3499590)Termination phase: Saturation
% 5.89/1.69 % (3499590)Time elapsed: 0.081 s
% 5.89/1.69 % (3499590)Peak memory usage: 91 MB
% 5.89/1.69 % (3499590)Instructions burned: 127 (million)
% 5.89/1.69 % (3499595)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=451669289:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 5.89/1.69 % (3499595)Instruction limit reached!
% 5.89/1.69 % (3499595)------------------------------
% 5.89/1.69 % (3499595)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.89/1.69 % (3499595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.89/1.69 % (3499595)CaDiCaL version: 2.1.3
% 5.89/1.69 % (3499595)Termination reason: Instruction limit
% 5.89/1.69 % (3499595)Termination phase: Saturation
% 5.89/1.69 % (3499595)Time elapsed: 0.073 s
% 5.89/1.69 % (3499595)Peak memory usage: 91 MB
% 5.89/1.69 % (3499595)Instructions burned: 194 (million)
% 5.89/1.69 % (3499596)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=4114100079:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 5.89/1.69 % (3499589)Refutation found. Thanks to Tanya!
% 5.89/1.69 % SZS status Unsatisfiable for theBenchmark
% 5.89/1.69 % SZS output start Proof for theBenchmark
% See solution above
% 5.89/1.70 % (3499589)------------------------------
% 5.89/1.70 % (3499589)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.89/1.70 % (3499589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.89/1.70 % (3499589)CaDiCaL version: 2.1.3
% 5.89/1.70 % (3499589)Termination reason: Refutation
% 5.89/1.70 % (3499589)Time elapsed: 0.036 s
% 5.89/1.70 % (3499589)Peak memory usage: 90 MB
% 5.89/1.70 % (3499589)Instructions burned: 57 (million)
% 5.89/1.70 % (3499589)------------------------------
% 5.89/1.70 % (3499589)------------------------------
% 5.89/1.70 % (3499438)Success in time 0.799 s
% 5.89/1.70 % Vampire exiting
%------------------------------------------------------------------------------