%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV603-1 : 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 : n009.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 01:19:04 PM UTC 2026
% Result : Unsatisfiable 0.19s 1.20s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 17 unt; 0 def)
% Number of atoms : 29 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 9 ( 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f627,axiom,
! [X0] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__abs2_0) ).
fof(f628,plain,
! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal)),
inference(reorient_equations,[],[f627]) ).
fof(f729,axiom,
! [X0] : c_Transcendental_Ocos(X0) = c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cos__sin__eq_0) ).
fof(f846,axiom,
! [X0] :
( c_NthRoot_Osqrt(X0) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| X0 = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__eq__1__iff_0) ).
fof(f847,plain,
! [X0] :
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X0)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X0 ),
inference(reorient_equations,[],[f846]) ).
fof(f970,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) = c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(f971,plain,
! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(reorient_equations,[],[f970]) ).
fof(f1045,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__zero__not__eq__one_0) ).
fof(f1178,negated_conjecture,
c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1179,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),
inference(reorient_equations,[],[f1178]) ).
fof(f1180,negated_conjecture,
c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1181,plain,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(reorient_equations,[],[f1180]) ).
fof(f1282,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1343,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(definition_unfolding,[],[f1179,f729]) ).
fof(f1344,plain,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),c_RealDef_Oreal(v_n,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(definition_unfolding,[],[f1181,f729]) ).
fof(f1408,plain,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[],[f1344,f1343]) ).
fof(f1528,plain,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(superposition,[],[f628,f1408]) ).
fof(f1548,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(superposition,[],[f847,f1528]) ).
fof(f1552,plain,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(trivial_inequality_removal,[],[f1548]) ).
fof(f1556,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[],[f1045,f1552]) ).
fof(f1867,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
inference(superposition,[],[f1556,f971]) ).
fof(f1877,plain,
~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(trivial_inequality_removal,[],[f1867]) ).
fof(f1884,plain,
$false,
inference(forward_subsumption_resolution,[],[f1877,f1282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV603-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n009.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 12:01:00 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 0.19/1.20 % (2988977)Input is clausal, will run a generic CNF schedule.
% 0.19/1.20 % (2988986)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3741178987:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.19/1.20 % (2988986)First to succeed.
% 0.19/1.20 % (2988986)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2988977"
% 0.19/1.20 % (2988983)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=631501774:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.19/1.20 % (2988985)lrs+10_1_sil=8000:sp=occurrence:random_seed=594370575:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.19/1.20 % (2988984)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=930829453:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.19/1.20 % (2988982)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=2651488678:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.19/1.20 % (2988988)dis-21_1_sil=8000:lcm=predicate:random_seed=119349556: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)
% 0.19/1.20 % (2988987)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4054724602:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.19/1.20 % (2988985)Also succeeded, but the first one will report.
% 0.19/1.20 % (2988988)Instruction limit reached!
% 0.19/1.20 % (2988988)------------------------------
% 0.19/1.20 % (2988988)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.20 % (2988988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.20 % (2988988)CaDiCaL version: 2.1.3
% 0.19/1.20 % (2988988)Termination reason: Instruction limit
% 0.19/1.20 % (2988988)Termination phase: Saturation
% 0.19/1.20 % (2988988)Time elapsed: 0.065 s
% 0.19/1.20 % (2988988)Peak memory usage: 89 MB
% 0.19/1.20 % (2988988)Instructions burned: 117 (million)
% 0.19/1.20 % (2988986)Refutation found. Thanks to Tanya!
% 0.19/1.20 % SZS status Unsatisfiable for theBenchmark
% 0.19/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.20 % (2988986)------------------------------
% 0.19/1.20 % (2988986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.20 % (2988986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.20 % (2988986)CaDiCaL version: 2.1.3
% 0.19/1.20 % (2988986)Termination reason: Refutation
% 0.19/1.20 % (2988986)Time elapsed: 0.018 s
% 0.19/1.20 % (2988986)Peak memory usage: 89 MB
% 0.19/1.20 % (2988986)Instructions burned: 54 (million)
% 0.19/1.20 % (2988986)------------------------------
% 0.19/1.20 % (2988986)------------------------------
% 0.19/1.20 % (2988977)Success in time 0.351 s
% 0.19/1.20 % Vampire exiting
%------------------------------------------------------------------------------