%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN011-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 10:19:10 AM UTC 2026
% Result : Unsatisfiable 8.64s 2.34s
% Output : Refutation 8.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 27 ( 21 unt; 0 def)
% Number of atoms : 43 ( 5 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 35 ( 19 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X0,X1] :
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_existence) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ quotient(X5,X4,X6)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X3,X5)
| ~ quotient(X0,X1,X2)
| ~ quotient(X2,X3,X7)
| less_equal(X6,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).
fof(f6,axiom,
! [X0,X1] :
( ~ less_equal(X1,X0)
| ~ less_equal(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_and_equal) ).
fof(f8,axiom,
! [X0,X1] : quotient(X0,X1,divide(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure) ).
fof(f14,axiom,
! [X2,X0,X1] :
( ~ less_equal(X1,X2)
| ~ less_equal(X0,X1)
| less_equal(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X4] :
( ~ quotient(X0,X3,X4)
| ~ less_equal(X2,X3)
| ~ quotient(X0,X1,X2)
| less_equal(X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQyLEz_implies_xQzLEy) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( ~ quotient(identity,X2,X3)
| ~ quotient(identity,X1,X2)
| ~ quotient(identity,X0,X1)
| X1 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_inversion_equals_three) ).
fof(f20,axiom,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).
fof(f21,axiom,
quotient(identity,b,idQb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_b) ).
fof(f22,axiom,
quotient(identity,idQb,idQ_idQb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQb) ).
fof(f23,axiom,
quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idQa_divide_idQ_idQb) ).
fof(f24,axiom,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).
fof(f25,axiom,
quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idQb_divide_idQ_idQa) ).
fof(f26,negated_conjecture,
idQa_Q__idQ_idQb != idQb_Q__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa) ).
fof(f152,plain,
idQa = divide(identity,idQ_idQa),
inference(unit_resulting_resolution,[],[f18,f8,f24,f20]) ).
fof(f174,plain,
idQb = divide(identity,idQ_idQb),
inference(unit_resulting_resolution,[],[f18,f8,f22,f21]) ).
fof(f199,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(unit_resulting_resolution,[],[f3,f8]) ).
fof(f4934,plain,
quotient(identity,idQ_idQb,idQb),
inference(superposition,[],[f8,f174]) ).
fof(f5261,plain,
quotient(identity,idQ_idQa,idQa),
inference(superposition,[],[f8,f152]) ).
fof(f11981,plain,
less_equal(divide(idQa,idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa)),
inference(unit_resulting_resolution,[],[f4,f8,f22,f8,f25,f5261]) ).
fof(f12118,plain,
less_equal(divide(idQa,idQb_Q__idQ_idQa),idQ_idQb),
inference(unit_resulting_resolution,[],[f14,f199,f11981]) ).
fof(f13653,plain,
less_equal(divide(idQb,idQa_Q__idQ_idQb),divide(idQ_idQa,idQ_idQb)),
inference(unit_resulting_resolution,[],[f4,f8,f24,f8,f23,f4934]) ).
fof(f13803,plain,
less_equal(divide(idQb,idQa_Q__idQ_idQb),idQ_idQa),
inference(unit_resulting_resolution,[],[f14,f199,f13653]) ).
fof(f13877,plain,
less_equal(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb),
inference(unit_resulting_resolution,[],[f15,f25,f8,f13803]) ).
fof(f13907,plain,
~ less_equal(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa),
inference(unit_resulting_resolution,[],[f6,f26,f13877]) ).
fof(f14034,plain,
~ less_equal(divide(idQa,idQb_Q__idQ_idQa),idQ_idQb),
inference(unit_resulting_resolution,[],[f15,f23,f8,f13907]) ).
fof(f14126,plain,
$false,
inference(forward_subsumption_resolution,[],[f14034,f12118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN011-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:51:17 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 6.54/2.01 % (3813756)Input is clausal, will run a generic CNF schedule.
% 6.54/2.01 % (3813872)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=500490269:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.54/2.01 % (3813873)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2881981907:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.54/2.01 % (3813876)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1148917600:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.54/2.01 % (3813874)lrs+10_1_sil=8000:sp=occurrence:random_seed=2570674357:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.54/2.01 % (3813877)dis-21_1_sil=8000:lcm=predicate:random_seed=3725884591: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)
% 6.54/2.01 % (3813875)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2786423090:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.54/2.01 % (3813871)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=150735762:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.54/2.01 % (3813874)Refutation not found, incomplete strategy
% 6.54/2.01 % (3813874)------------------------------
% 6.54/2.01 % (3813874)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.54/2.01 % (3813874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.54/2.01 % (3813874)CaDiCaL version: 2.1.3
% 6.54/2.01 % (3813874)Termination reason: Refutation not found, incomplete strategy
% 6.54/2.01 % (3813874)Time elapsed: 0.058 s
% 6.54/2.01 % (3813874)Peak memory usage: 89 MB
% 6.54/2.01 % (3813874)Instructions burned: 92 (million)
% 6.54/2.01 % (3813877)Instruction limit reached!
% 6.54/2.01 % (3813877)------------------------------
% 6.54/2.01 % (3813877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.54/2.01 % (3813877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.54/2.01 % (3813877)CaDiCaL version: 2.1.3
% 6.54/2.01 % (3813877)Termination reason: Instruction limit
% 6.54/2.01 % (3813877)Termination phase: Saturation
% 6.54/2.01 % (3813877)Time elapsed: 0.065 s
% 6.54/2.01 % (3813877)Peak memory usage: 88 MB
% 6.54/2.01 % (3813877)Instructions burned: 118 (million)
% 6.54/2.01 % (3813875)Instruction limit reached!
% 6.54/2.01 % (3813875)------------------------------
% 6.54/2.01 % (3813875)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.54/2.01 % (3813875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.54/2.01 % (3813875)CaDiCaL version: 2.1.3
% 6.54/2.01 % (3813875)Termination reason: Instruction limit
% 6.54/2.01 % (3813875)Termination phase: Saturation
% 6.54/2.01 % (3813875)Time elapsed: 0.070 s
% 6.54/2.01 % (3813875)Peak memory usage: 88 MB
% 6.54/2.01 % (3813875)Instructions burned: 116 (million)
% 6.54/2.01 % (3813876)Instruction limit reached!
% 6.54/2.01 % (3813876)------------------------------
% 6.54/2.01 % (3813876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.54/2.01 % (3813876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.54/2.01 % (3813876)CaDiCaL version: 2.1.3
% 6.54/2.01 % (3813876)Termination reason: Instruction limit
% 6.54/2.01 % (3813876)Termination phase: Saturation
% 6.54/2.01 % (3813876)Time elapsed: 0.100 s
% 6.54/2.01 % (3813876)Peak memory usage: 89 MB
% 6.54/2.01 % (3813876)Instructions burned: 181 (million)
% 6.54/2.01 % (3813901)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2717430692: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)
% 6.54/2.01 % (3813900)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=216193925:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 6.54/2.01 % (3813900)Refutation not found, incomplete strategy
% 6.54/2.01 % (3813900)------------------------------
% 6.54/2.01 % (3813900)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.54/2.01 % (3813900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.54/2.01 % (3813900)CaDiCaL version: 2.1.3
% 8.64/2.34 % (3813900)Termination reason: Refutation not found, incomplete strategy
% 8.64/2.34 % (3813900)Time elapsed: 0.035 s
% 8.64/2.34 % (3813900)Peak memory usage: 88 MB
% 8.64/2.34 % (3813900)Instructions burned: 49 (million)
% 8.64/2.34 % (3813902)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1656085175:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 8.64/2.34 % (3813874)------------------------------
% 8.64/2.34 % (3813874)------------------------------
% 8.64/2.34 % (3813901)Instruction limit reached!
% 8.64/2.34 % (3813901)------------------------------
% 8.64/2.34 % (3813901)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.34 % (3813901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.34 % (3813901)CaDiCaL version: 2.1.3
% 8.64/2.34 % (3813901)Termination reason: Instruction limit
% 8.64/2.34 % (3813901)Termination phase: Saturation
% 8.64/2.34 % (3813901)Time elapsed: 0.144 s
% 8.64/2.34 % (3813901)Peak memory usage: 88 MB
% 8.64/2.34 % (3813901)Instructions burned: 189 (million)
% 8.64/2.34 % (3813902)Instruction limit reached!
% 8.64/2.34 % (3813902)------------------------------
% 8.64/2.34 % (3813902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.34 % (3813902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.34 % (3813902)CaDiCaL version: 2.1.3
% 8.64/2.34 % (3813902)Termination reason: Instruction limit
% 8.64/2.34 % (3813902)Termination phase: Saturation
% 8.64/2.34 % (3813902)Time elapsed: 0.199 s
% 8.64/2.34 % (3813902)Peak memory usage: 89 MB
% 8.64/2.34 % (3813902)Instructions burned: 220 (million)
% 8.64/2.34 % (3813937)lrs+10_64_to=lpo:sil=8000:random_seed=935633985:i=126:bd=preordered_2994 on theBenchmark for (2994ds/126Mi)
% 8.64/2.34 % (3813900)------------------------------
% 8.64/2.34 % (3813900)------------------------------
% 8.64/2.34 % (3813938)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=4052041752:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 8.64/2.34 % (3813872)First to succeed.
% 8.64/2.34 % (3813872)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3813756"
% 8.64/2.34 % (3813939)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3753332400:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 8.64/2.34 % (3813937)Instruction limit reached!
% 8.64/2.34 % (3813937)------------------------------
% 8.64/2.34 % (3813937)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.34 % (3813937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.34 % (3813937)CaDiCaL version: 2.1.3
% 8.64/2.34 % (3813937)Termination reason: Instruction limit
% 8.64/2.34 % (3813937)Termination phase: Saturation
% 8.64/2.34 % (3813937)Time elapsed: 0.136 s
% 8.64/2.34 % (3813937)Peak memory usage: 88 MB
% 8.64/2.34 % (3813937)Instructions burned: 126 (million)
% 8.64/2.34 % (3813938)Instruction limit reached!
% 8.64/2.34 % (3813938)------------------------------
% 8.64/2.34 % (3813938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.34 % (3813938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.34 % (3813938)CaDiCaL version: 2.1.3
% 8.64/2.34 % (3813938)Termination reason: Instruction limit
% 8.64/2.34 % (3813938)Termination phase: Saturation
% 8.64/2.34 % (3813938)Time elapsed: 0.207 s
% 8.64/2.34 % (3813938)Peak memory usage: 90 MB
% 8.64/2.34 % (3813938)Instructions burned: 194 (million)
% 8.64/2.34 % (3813939)Instruction limit reached!
% 8.64/2.34 % (3813939)------------------------------
% 8.64/2.34 % (3813939)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.34 % (3813939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.34 % (3813939)CaDiCaL version: 2.1.3
% 8.64/2.34 % (3813939)Termination reason: Instruction limit
% 8.64/2.34 % (3813939)Termination phase: Saturation
% 8.64/2.34 % (3813939)Time elapsed: 0.170 s
% 8.64/2.34 % (3813939)Peak memory usage: 90 MB
% 8.64/2.34 % (3813939)Instructions burned: 157 (million)
% 8.64/2.34 % (3813872)Refutation found. Thanks to Tanya!
% 8.64/2.34 % SZS status Unsatisfiable for theBenchmark
% 8.64/2.34 % SZS output start Proof for theBenchmark
% See solution above
% 8.64/2.34 % (3813872)------------------------------
% 8.64/2.34 % (3813872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.34 % (3813872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.34 % (3813872)CaDiCaL version: 2.1.3
% 8.64/2.34 % (3813872)Termination reason: Refutation
% 8.64/2.34 % (3813872)Time elapsed: 0.730 s
% 8.64/2.34 % (3813872)Peak memory usage: 131 MB
% 8.64/2.34 % (3813872)Instructions burned: 1623 (million)
% 8.64/2.34 % (3813872)------------------------------
% 8.64/2.34 % (3813872)------------------------------
% 8.64/2.34 % (3813756)Success in time 1.146 s
% 8.64/2.34 % Vampire exiting
%------------------------------------------------------------------------------