%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG001-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:35:03 PM UTC 2026
% Result : Unsatisfiable 0.31s 2.71s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 27 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 66 ( 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f3,axiom,
! [X0] : sum(additive_identity,X0,X0) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
fof(f4,axiom,
! [X0] : sum(X0,additive_identity,X0) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f5,plain,
! [X0] : true = sum(X0,additive_identity,X0),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f7,plain,
! [X0,X1] : true = product(X0,X1,multiply(X0,X1)),
inference(reorient_equations,[],[f6]) ).
fof(f24,axiom,
! [X2,X3,X0,X1,X6,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(product(X0,X5,X6),true,ifeq(sum(X5,X3,X1),true,sum(X6,X4,X2),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f25,plain,
! [X2,X3,X0,X1,X6,X4,X5] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(product(X0,X5,X6),true,ifeq(sum(X5,X3,X1),true,sum(X6,X4,X2),true),true),true),true),
inference(reorient_equations,[],[f24]) ).
fof(f35,axiom,
! [X2,X3,X0,X1] : ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X3,X1,X2),true,X3,X0),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation2) ).
fof(f36,negated_conjecture,
product(a,additive_identity,additive_identity) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_times_additive_id_is_additive_id) ).
fof(f37,plain,
true != product(a,additive_identity,additive_identity),
inference(reorient_equations,[],[f36]) ).
fof(f73,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X0,additive_identity,X3),true,ifeq(product(X0,X1,X4),true,ifeq(true,true,sum(X4,X3,X2),true),true),true),true),
inference(superposition,[],[f25,f5]) ).
fof(f84,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X0,additive_identity,X3),true,ifeq(product(X0,X1,X4),true,sum(X4,X3,X2),true),true),true),
inference(forward_demodulation,[],[f73,f2]) ).
fof(f167,plain,
! [X0,X1] : additive_identity = ifeq2(true,true,ifeq2(sum(X1,X0,X0),true,X1,additive_identity),additive_identity),
inference(superposition,[],[f35,f3]) ).
fof(f180,plain,
! [X0,X1] : additive_identity = ifeq2(sum(X1,X0,X0),true,X1,additive_identity),
inference(forward_demodulation,[],[f167,f1]) ).
fof(f396,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X0,additive_identity,X3),true,ifeq(true,true,sum(multiply(X0,X1),X3,X2),true),true),true),
inference(superposition,[],[f84,f7]) ).
fof(f403,plain,
! [X2,X3,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X0,additive_identity,X3),true,sum(multiply(X0,X1),X3,X2),true),true),
inference(forward_demodulation,[],[f396,f2]) ).
fof(f1152,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(product(X0,additive_identity,X2),true,sum(multiply(X0,X1),X2,multiply(X0,X1)),true),true),
inference(superposition,[],[f403,f7]) ).
fof(f1181,plain,
! [X2,X0,X1] : true = ifeq(product(X0,additive_identity,X2),true,sum(multiply(X0,X1),X2,multiply(X0,X1)),true),
inference(forward_demodulation,[],[f1152,f2]) ).
fof(f1285,plain,
! [X0,X1] : true = ifeq(true,true,sum(multiply(X0,X1),multiply(X0,additive_identity),multiply(X0,X1)),true),
inference(superposition,[],[f1181,f7]) ).
fof(f1306,plain,
! [X0,X1] : true = sum(multiply(X0,X1),multiply(X0,additive_identity),multiply(X0,X1)),
inference(forward_demodulation,[],[f1285,f2]) ).
fof(f1318,plain,
! [X0] : additive_identity = ifeq2(true,true,multiply(X0,additive_identity),additive_identity),
inference(superposition,[],[f180,f1306]) ).
fof(f1389,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(forward_demodulation,[],[f1318,f1]) ).
fof(f1403,plain,
! [X0] : true = product(X0,additive_identity,additive_identity),
inference(superposition,[],[f7,f1389]) ).
fof(f1494,plain,
true != true,
inference(superposition,[],[f37,f1403]) ).
fof(f1495,plain,
$false,
inference(trivial_inequality_removal,[],[f1494]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG001-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.49 % Computer : n009.cluster.edu
% 0.22/0.49 % Model : x86_64 x86_64
% 0.22/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.49 % Memory : 8046.5625MB
% 0.22/0.49 % OS : Linux 6.8.0-71-generic
% 0.22/0.49 % CPULimit : 300
% 0.22/0.49 % WCLimit : 300
% 0.22/0.49 % DateTime : Sun Sep 27 22:57:45 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.49 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.55 Running first-order theorem proving
% 0.27/0.55 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
% 0.31/2.71 % (2501679)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.31/2.71 % (2501685)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=3636429341:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.31/2.71 % (2501684)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=1610186782:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.31/2.71 % (2501687)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3940494590:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.31/2.71 % (2501688)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1765996072:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.31/2.71 % (2501686)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4197262992:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.31/2.71 % (2501690)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4011260001:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.31/2.71 % (2501689)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=22628591:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.31/2.71 % (2501687)Instruction limit reached!
% 0.31/2.71 % (2501687)------------------------------
% 0.31/2.71 % (2501687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.31/2.71 % (2501687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/2.71 % (2501687)CaDiCaL version: 2.1.3
% 0.31/2.71 % (2501687)Termination reason: Instruction limit
% 0.31/2.71 % (2501687)Termination phase: Saturation
% 0.31/2.71 % (2501687)Time elapsed: 0.134 s
% 0.31/2.71 % (2501687)Peak memory usage: 89 MB
% 0.31/2.71 % (2501687)Instructions burned: 136 (million)
% 0.31/2.71 % (2501688)Instruction limit reached!
% 0.31/2.71 % (2501688)------------------------------
% 0.31/2.71 % (2501688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.31/2.71 % (2501688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/2.71 % (2501688)CaDiCaL version: 2.1.3
% 0.31/2.71 % (2501688)Termination reason: Instruction limit
% 0.31/2.71 % (2501688)Termination phase: Saturation
% 0.31/2.71 % (2501688)Time elapsed: 0.176 s
% 0.31/2.71 % (2501688)Peak memory usage: 89 MB
% 0.31/2.71 % (2501688)Instructions burned: 181 (million)
% 0.31/2.71 % (2501689)Instruction limit reached!
% 0.31/2.71 % (2501689)------------------------------
% 0.31/2.71 % (2501689)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.31/2.71 % (2501689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/2.71 % (2501689)CaDiCaL version: 2.1.3
% 0.31/2.71 % (2501689)Termination reason: Instruction limit
% 0.31/2.71 % (2501689)Termination phase: Saturation
% 0.31/2.71 % (2501689)Time elapsed: 0.262 s
% 0.31/2.71 % (2501689)Peak memory usage: 91 MB
% 0.31/2.71 % (2501689)Instructions burned: 257 (million)
% 0.31/2.71 % (2501698)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2788320246:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 0.31/2.71 % (2501699)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2402897827:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 0.31/2.71 % (2501700)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1504238526:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 0.31/2.71 % (2501700)Instruction limit reached!
% 0.31/2.71 % (2501700)------------------------------
% 0.31/2.71 % (2501700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.31/2.71 % (2501700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/2.71 % (2501700)CaDiCaL version: 2.1.3
% 0.31/2.71 % (2501700)Termination reason: Instruction limit
% 0.31/2.71 % (2501700)Termination phase: Saturation
% 0.31/2.71 % (2501700)Time elapsed: 0.191 s
% 0.31/2.71 % (2501700)Peak memory usage: 90 MB
% 0.31/2.71 % (2501700)Instructions burned: 216 (million)
% 0.31/2.71 % (2501685)First to succeed.
% 0.31/2.71 % (2501685)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2501679"
% 0.31/2.71 % (2501704)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=3557563141:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2990 on theBenchmark for (2990ds/317Mi)
% 0.31/2.71 % (2501685)Refutation found. Thanks to Tanya!
% 0.31/2.71 % SZS status Unsatisfiable for theBenchmark
% 0.31/2.71 % SZS output start Proof for theBenchmark
% See solution above
% 0.31/2.71 % (2501685)------------------------------
% 0.31/2.71 % (2501685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.31/2.71 % (2501685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/2.71 % (2501685)CaDiCaL version: 2.1.3
% 0.31/2.71 % (2501685)Termination reason: Refutation
% 0.31/2.71 % (2501685)Time elapsed: 0.786 s
% 0.31/2.71 % (2501685)Peak memory usage: 132 MB
% 0.31/2.71 % (2501685)Instructions burned: 1300 (million)
% 0.31/2.71 % (2501685)------------------------------
% 0.31/2.71 % (2501685)------------------------------
% 0.31/2.71 % (2501679)Success in time 1.205 s
% 0.31/2.71 % Vampire exiting
%------------------------------------------------------------------------------