%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG377-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 09:30:26 AM UTC 2026
% Result : Unsatisfiable 2.59s 0.66s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 10 unt; 0 def)
% Number of atoms : 14 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 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 : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f547,axiom,
! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_Suc(X1),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
fof(f548,plain,
! [X0,X1] : c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(X0,c_Suc(X1),tc_nat),
inference(reorient_equations,[],[f547]) ).
fof(f579,axiom,
! [X2,X0,X1] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__left__mono_0) ).
fof(f623,axiom,
c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f624,negated_conjecture,
~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1047,plain,
! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(X1,X2,tc_RealDef_Oreal) ),
inference(consistent_polarity_flipping,[],[f579]) ).
fof(f1072,plain,
~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(consistent_polarity_flipping,[],[f623]) ).
fof(f1073,plain,
c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(consistent_polarity_flipping,[],[f624]) ).
fof(f3724,plain,
c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[],[f1047,f1073]) ).
fof(f3741,plain,
c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_HOL_Oplus__class_Oplus(v_N1____,c_Suc(v_N2____),tc_nat),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f3724,f548]) ).
fof(f8129,plain,
~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_nat),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(c_HOL_Oplus__class_Oplus(v_N1____,c_Suc(v_N2____),tc_nat),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f1072,f548]) ).
fof(f8790,plain,
$false,
inference(forward_subsumption_resolution,[],[f3741,f8129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG377-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.24 % Computer : n018.cluster.edu
% 0.12/0.24 % Model : x86_64 x86_64
% 0.12/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.24 % Memory : 8046.5625MB
% 0.12/0.24 % OS : Linux 6.8.0-71-generic
% 0.12/0.24 % CPULimit : 300
% 0.12/0.24 % WCLimit : 300
% 0.12/0.24 % DateTime : Mon Sep 28 20:16:26 UTC 2026
% 0.12/0.24 % CPUTime :
% 0.12/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.27 Running first-order model finding
% 0.12/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.59/0.66 % (3722580)Will run a generic schedule for satisfiability detection.
% 2.59/0.66 % (3722589)dis+10_1_sil=32000:sp=arity:random_seed=2439047307:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.59/0.66 % (3722587)% WARNING: option uhcvi not known.
% 2.59/0.66 % (3722587)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2702520353:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.59/0.66 % (3722586)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1729853617_2999 on theBenchmark for (2999ds/0Mi)
% 2.59/0.66 % (3722592)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1497415068:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.59/0.66 % (3722591)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=714582540:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.59/0.66 % (3722588)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2909656043:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.59/0.66 % (3722590)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1143344679:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.59/0.66 % (3722589)Instruction limit reached!
% 2.59/0.66 % (3722589)------------------------------
% 2.59/0.66 % (3722589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.66 % (3722589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.66 % (3722589)CaDiCaL version: 2.1.3
% 2.59/0.66 % (3722589)Termination reason: Instruction limit
% 2.59/0.66 % (3722589)Termination phase: Saturation
% 2.59/0.66 % (3722589)Time elapsed: 0.039 s
% 2.59/0.66 % (3722589)Peak memory usage: 12 MB
% 2.59/0.66 % (3722589)Instructions burned: 104 (million)
% 2.59/0.66 % (3722601)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4055349026:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.59/0.66 % TRYING [1]
% 2.59/0.66 % TRYING [2]
% 2.59/0.66 % TRYING [1]
% 2.59/0.66 % TRYING [2]
% 2.59/0.66 % TRYING [3]
% 2.59/0.66 % TRYING [3]
% 2.59/0.66 % (3722590)Instruction limit reached!
% 2.59/0.66 % (3722590)------------------------------
% 2.59/0.66 % (3722590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.66 % (3722590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.66 % (3722590)CaDiCaL version: 2.1.3
% 2.59/0.66 % (3722590)Termination reason: Instruction limit
% 2.59/0.66 % (3722590)Termination phase: Saturation
% 2.59/0.66 % (3722590)Time elapsed: 0.125 s
% 2.59/0.66 % (3722590)Peak memory usage: 13 MB
% 2.59/0.66 % (3722590)Instructions burned: 117 (million)
% 2.59/0.66 % (3722604)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2736263308:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.59/0.66 % (3722591)Instruction limit reached!
% 2.59/0.66 % (3722591)------------------------------
% 2.59/0.66 % (3722591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.66 % (3722591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.66 % (3722591)CaDiCaL version: 2.1.3
% 2.59/0.66 % (3722591)Termination reason: Instruction limit
% 2.59/0.66 % (3722591)Termination phase: Saturation
% 2.59/0.66 % (3722591)Time elapsed: 0.167 s
% 2.59/0.66 % (3722591)Peak memory usage: 13 MB
% 2.59/0.66 % (3722591)Instructions burned: 131 (million)
% 2.59/0.66 % (3722592)Instruction limit reached!
% 2.59/0.66 % (3722592)------------------------------
% 2.59/0.66 % (3722592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.66 % (3722592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.66 % (3722592)CaDiCaL version: 2.1.3
% 2.59/0.66 % (3722592)Termination reason: Instruction limit
% 2.59/0.66 % (3722592)Termination phase: Saturation
% 2.59/0.66 % (3722592)Time elapsed: 0.177 s
% 2.59/0.66 % (3722592)Peak memory usage: 14 MB
% 2.59/0.66 % (3722592)Instructions burned: 159 (million)
% 2.59/0.66 % (3722607)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1525449635:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2997 on theBenchmark for (2997ds/684Mi)
% 2.59/0.66 % (3722608)ott-21_1_sil=16000:fs=off:random_seed=1093152968:i=180:av=off:fsr=off_2997 on theBenchmark for (2997ds/180Mi)
% 2.59/0.66 % TRYING [4]
% 2.59/0.66 % (3722601)Instruction limit reached!
% 2.59/0.66 % (3722601)------------------------------
% 2.59/0.66 % (3722601)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.66 % (3722601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.66 % (3722601)CaDiCaL version: 2.1.3
% 2.59/0.66 % (3722601)Termination reason: Instruction limit
% 2.59/0.66 % (3722601)Termination phase: Finite model building constraint generation
% 2.59/0.66 % (3722601)Time elapsed: 0.240 s
% 2.59/0.66 % (3722601)Peak memory usage: 37 MB
% 2.59/0.66 % (3722601)Instructions burned: 717 (million)
% 2.59/0.66 % (3722614)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4219757009:i=477:bd=all_2996 on theBenchmark for (2996ds/477Mi)
% 2.59/0.66 % (3722604)Instruction limit reached!
% 2.59/0.66 % (3722604)------------------------------
% 2.59/0.66 % (3722604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.66 % (3722604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.66 % (3722604)CaDiCaL version: 2.1.3
% 2.59/0.66 % (3722604)Termination reason: Instruction limit
% 2.59/0.66 % (3722604)Termination phase: Saturation
% 2.59/0.66 % (3722604)Time elapsed: 0.150 s
% 2.59/0.66 % (3722604)Peak memory usage: 13 MB
% 2.59/0.66 % (3722604)Instructions burned: 131 (million)
% 2.59/0.66 % (3722587) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3722580-3722587"...
% 2.59/0.66 % (3722587)...printing done.
% 2.59/0.66 % (3722617)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2813987206:fmbsr=1.3:i=865:ins=25_2996 on theBenchmark for (2996ds/865Mi)
% 2.59/0.66 % (3722587)Refutation found. Thanks to Tanya!
% 2.59/0.66 % SZS status Unsatisfiable for theBenchmark
% 2.59/0.66 % SZS output start Proof for theBenchmark
% See solution above
% 2.59/0.66 % (3722587)------------------------------
% 2.59/0.66 % (3722587)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.66 % (3722587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.66 % (3722587)CaDiCaL version: 2.1.3
% 2.59/0.66 % (3722587)Termination reason: Refutation
% 2.59/0.66 % (3722587)Time elapsed: 0.338 s
% 2.59/0.66 % (3722587)Peak memory usage: 15 MB
% 2.59/0.66 % (3722587)Instructions burned: 361 (million)
% 2.59/0.66 % (3722580)Success in time 0.382 s
% 2.59/0.66 % Vampire exiting
%------------------------------------------------------------------------------