%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA133-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 09:31:10 AM UTC 2026
% Result : Unsatisfiable 9.44s 2.34s
% Output : Refutation 9.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_plus) ).
fof(f2,axiom,
! [X2,X0,X1] : '+'(X0,'+'(X1,X2)) = '+'('+'(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associtivity_of_plus) ).
fof(f3,axiom,
! [X0,X1] : times(X0,X1) = times(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_times) ).
fof(f5,axiom,
! [X0] : '+'(zero,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_zero) ).
fof(f8,axiom,
! [X0] : times(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_one) ).
fof(f10,axiom,
! [X0] : '+'(X0,minus(X0)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minus) ).
fof(f11,plain,
! [X0] : zero = '+'(X0,minus(X0)),
inference(reorient_equations,[],[f10]) ).
fof(f16,axiom,
d(x) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_x) ).
fof(f17,plain,
one = d(x),
inference(reorient_equations,[],[f16]) ).
fof(f18,axiom,
! [X0,X1] : d('+'(X0,X1)) = '+'(d(X0),d(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_plus) ).
fof(f19,axiom,
! [X0,X1] : d(times(X0,X1)) = '+'(times(X0,d(X1)),times(X1,d(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_times) ).
fof(f20,axiom,
! [X0] : d(sin(X0)) = times(cos(X0),d(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_sin) ).
fof(f21,axiom,
! [X0] : d(cos(X0)) = minus(times(sin(X0),d(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',derivative_of_cos) ).
fof(f22,negated_conjecture,
! [X0] : d(X0) != times(x,cos(x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f26,plain,
! [X0] : times(X0,one) = X0,
inference(superposition,[],[f3,f8]) ).
fof(f29,plain,
d(sin(x)) = times(cos(x),one),
inference(superposition,[],[f20,f17]) ).
fof(f34,plain,
d(sin(x)) = times(one,cos(x)),
inference(forward_demodulation,[],[f29,f3]) ).
fof(f35,plain,
cos(x) = d(sin(x)),
inference(forward_demodulation,[],[f34,f8]) ).
fof(f39,plain,
! [X0] : '+'(X0,zero) = X0,
inference(superposition,[],[f5,f1]) ).
fof(f44,plain,
d(cos(x)) = minus(times(sin(x),one)),
inference(superposition,[],[f21,f17]) ).
fof(f49,plain,
d(cos(x)) = minus(times(one,sin(x))),
inference(forward_demodulation,[],[f44,f3]) ).
fof(f51,plain,
d(cos(x)) = minus(sin(x)),
inference(forward_demodulation,[],[f49,f8]) ).
fof(f61,plain,
! [X0] : d(times(x,X0)) = '+'(times(x,d(X0)),times(X0,one)),
inference(superposition,[],[f19,f17]) ).
fof(f72,plain,
! [X0] : '+'(times(X0,one),times(x,d(X0))) = d(times(x,X0)),
inference(forward_demodulation,[],[f61,f1]) ).
fof(f79,plain,
! [X0] : d(times(x,X0)) = '+'(X0,times(x,d(X0))),
inference(forward_demodulation,[],[f72,f26]) ).
fof(f222,plain,
! [X0,X1] : '+'(X0,'+'(minus(X0),X1)) = '+'(zero,X1),
inference(superposition,[],[f2,f11]) ).
fof(f241,plain,
! [X0,X1] : '+'(X0,'+'(minus(X0),X1)) = X1,
inference(forward_demodulation,[],[f222,f5]) ).
fof(f248,plain,
! [X0] : '+'(X0,zero) = minus(minus(X0)),
inference(superposition,[],[f241,f11]) ).
fof(f257,plain,
! [X0] : minus(minus(X0)) = X0,
inference(forward_demodulation,[],[f248,f39]) ).
fof(f293,plain,
sin(x) = minus(d(cos(x))),
inference(superposition,[],[f257,f51]) ).
fof(f775,plain,
! [X0] : times(x,d(minus(X0))) = '+'(X0,d(times(x,minus(X0)))),
inference(superposition,[],[f241,f79]) ).
fof(f1139,plain,
times(x,d(sin(x))) = '+'(d(cos(x)),d(times(x,sin(x)))),
inference(superposition,[],[f775,f293]) ).
fof(f1169,plain,
times(x,d(sin(x))) = d('+'(cos(x),times(x,sin(x)))),
inference(forward_demodulation,[],[f1139,f18]) ).
fof(f1178,plain,
times(x,cos(x)) = d('+'(cos(x),times(x,sin(x)))),
inference(forward_demodulation,[],[f1169,f35]) ).
fof(f1186,plain,
$false,
inference(forward_subsumption_resolution,[],[f1178,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA133-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.28 % Computer : n020.cluster.edu
% 0.23/0.28 % Model : x86_64 x86_64
% 0.23/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.28 % Memory : 8046.5625MB
% 0.23/0.28 % OS : Linux 6.8.0-71-generic
% 0.23/0.28 % CPULimit : 300
% 0.23/0.28 % WCLimit : 300
% 0.23/0.28 % DateTime : Mon Sep 28 20:39:34 UTC 2026
% 0.23/0.28 % CPUTime :
% 0.23/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.32 Running first-order theorem proving
% 0.23/0.32 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
% 9.44/2.34 % (509287)Detected a unit-equality problem, will run specialized UEQ schedule.
% 9.44/2.34 % (509299)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=890301137:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 9.44/2.34 % (509294)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=4158211128:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 9.44/2.34 % (509300)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4008550682:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 9.44/2.34 % (509297)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4076765343:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 9.44/2.34 % (509298)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3880262749:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 9.44/2.34 % (509296)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=180626448:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 9.44/2.34 % (509295)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=4103886957:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 9.44/2.34 % (509297)Instruction limit reached!
% 9.44/2.34 % (509297)------------------------------
% 9.44/2.34 % (509297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.44/2.34 % (509297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.44/2.34 % (509297)CaDiCaL version: 2.1.3
% 9.44/2.34 % (509297)Termination reason: Instruction limit
% 9.44/2.34 % (509297)Termination phase: Saturation
% 9.44/2.34 % (509297)Time elapsed: 0.136 s
% 9.44/2.34 % (509297)Peak memory usage: 89 MB
% 9.44/2.34 % (509297)Instructions burned: 136 (million)
% 9.44/2.34 % (509299)Instruction limit reached!
% 9.44/2.34 % (509299)------------------------------
% 9.44/2.34 % (509299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.44/2.34 % (509299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.44/2.34 % (509299)CaDiCaL version: 2.1.3
% 9.44/2.34 % (509299)Termination reason: Instruction limit
% 9.44/2.34 % (509299)Termination phase: Saturation
% 9.44/2.34 % (509299)Time elapsed: 0.228 s
% 9.44/2.34 % (509299)Peak memory usage: 90 MB
% 9.44/2.34 % (509299)Instructions burned: 257 (million)
% 9.44/2.34 % (509298)Instruction limit reached!
% 9.44/2.34 % (509298)------------------------------
% 9.44/2.34 % (509298)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.44/2.34 % (509298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.44/2.34 % (509298)CaDiCaL version: 2.1.3
% 9.44/2.34 % (509298)Termination reason: Instruction limit
% 9.44/2.34 % (509298)Termination phase: Saturation
% 9.44/2.34 % (509298)Time elapsed: 0.168 s
% 9.44/2.34 % (509298)Peak memory usage: 89 MB
% 9.44/2.34 % (509298)Instructions burned: 182 (million)
% 9.44/2.34 % (509308)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2460966892:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 9.44/2.34 % (509310)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3484486207:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 9.44/2.34 % (509309)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=332792301:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 9.44/2.34 % (509310)Instruction limit reached!
% 9.44/2.34 % (509310)------------------------------
% 9.44/2.34 % (509310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.44/2.34 % (509310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.44/2.34 % (509310)CaDiCaL version: 2.1.3
% 9.44/2.34 % (509310)Termination reason: Instruction limit
% 9.44/2.34 % (509310)Termination phase: Saturation
% 9.44/2.34 % (509310)Time elapsed: 0.204 s
% 9.44/2.34 % (509310)Peak memory usage: 89 MB
% 9.44/2.34 % (509310)Instructions burned: 215 (million)
% 9.44/2.34 % (509295)First to succeed.
% 9.44/2.34 % (509295)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-509287"
% 9.44/2.34 % (509314)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=4249788800:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2991 on theBenchmark for (2991ds/317Mi)
% 9.44/2.34 % (509295)Refutation found. Thanks to Tanya!
% 9.44/2.34 % SZS status Unsatisfiable for theBenchmark
% 9.44/2.34 % SZS output start Proof for theBenchmark
% See solution above
% 9.44/2.34 % (509295)------------------------------
% 9.44/2.34 % (509295)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.44/2.34 % (509295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.44/2.34 % (509295)CaDiCaL version: 2.1.3
% 9.44/2.34 % (509295)Termination reason: Refutation
% 9.44/2.34 % (509295)Time elapsed: 0.683 s
% 9.44/2.34 % (509295)Peak memory usage: 129 MB
% 9.44/2.34 % (509295)Instructions burned: 1059 (million)
% 9.44/2.34 % (509295)------------------------------
% 9.44/2.34 % (509295)------------------------------
% 9.44/2.34 % (509287)Success in time 1.218 s
% 9.44/2.34 % Vampire exiting
%------------------------------------------------------------------------------