%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU997^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 : Wed Sep 30 08:34:31 AM UTC 2026
% Result : Theorem 1.10s 0.41s
% Output : Refutation 1.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU997^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n014.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 14:57:15 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 1.10/0.41 % (2772909)Will run a generic schedule for satisfiability detection.
% 1.10/0.41 % (2772918)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1039123173:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.10/0.41 % (2772918)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.10/0.41 % (2772915)% WARNING: option uhcvi not known.
% 1.10/0.41 % (2772914)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1810600167_2999 on theBenchmark for (2999ds/0Mi)
% 1.10/0.41 % (2772915)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2074089093:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.10/0.41 % (2772916)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2425694574:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.10/0.41 % (2772917)dis+10_1_sil=32000:sp=arity:random_seed=1523507025:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.10/0.41 % (2772920)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=453184724:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.10/0.41 % (2772915)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.10/0.41 % Exception at run slice level
% 1.10/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.10/0.41 % (2772915)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.10/0.41 % (2772919)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=590998419:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.10/0.41 % (2772927)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1829633907:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.10/0.41 % Exception at run slice level
% 1.10/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.10/0.41 % (2772918)Instruction limit reached!
% 1.10/0.41 % (2772918)------------------------------
% 1.10/0.41 % (2772918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.41 % (2772918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.41 % (2772918)CaDiCaL version: 2.1.3
% 1.10/0.41 % (2772918)Termination reason: Instruction limit
% 1.10/0.41 % (2772918)Termination phase: Saturation
% 1.10/0.41 % (2772918)Time elapsed: 0.032 s
% 1.10/0.41 % (2772918)Peak memory usage: 12 MB
% 1.10/0.41 % (2772918)Instructions burned: 119 (million)
% 1.10/0.41 % (2772931)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=1264616280:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.10/0.41 % (2772931)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.10/0.41 % (2772931)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.10/0.41 % (2772930)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1735603330:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.10/0.41 % (2772917)Instruction limit reached!
% 1.10/0.41 % (2772917)------------------------------
% 1.10/0.41 % (2772917)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.41 % (2772917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.41 % (2772917)CaDiCaL version: 2.1.3
% 1.10/0.41 % (2772917)Termination reason: Instruction limit
% 1.10/0.41 % (2772917)Termination phase: Saturation
% 1.10/0.41 % (2772917)Time elapsed: 0.051 s
% 1.10/0.41 % (2772917)Peak memory usage: 12 MB
% 1.10/0.41 % (2772917)Instructions burned: 104 (million)
% 1.10/0.41 % (2772934)ott-21_1_sil=16000:fs=off:random_seed=2369217994:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.10/0.41 % (2772920)Instruction limit reached!
% 1.10/0.41 % (2772920)------------------------------
% 1.10/0.41 % (2772920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.41 % (2772920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.41 % (2772920)CaDiCaL version: 2.1.3
% 1.10/0.41 % (2772920)Termination reason: Instruction limit
% 1.10/0.41 % (2772920)Termination phase: Saturation
% 1.10/0.41 % (2772920)Time elapsed: 0.079 s
% 1.10/0.41 % (2772920)Peak memory usage: 12 MB
% 1.10/0.41 % (2772920)Instructions burned: 161 (million)
% 1.10/0.41 % (2772936)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=908026084:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.10/0.41 % (2772930)Instruction limit reached!
% 1.10/0.41 % (2772930)------------------------------
% 1.10/0.41 % (2772930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.41 % (2772930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.41 % (2772930)CaDiCaL version: 2.1.3
% 1.10/0.41 % (2772930)Termination reason: Instruction limit
% 1.10/0.41 % (2772930)Termination phase: Saturation
% 1.10/0.41 % (2772930)Time elapsed: 0.067 s
% 1.10/0.41 % (2772930)Peak memory usage: 12 MB
% 1.10/0.41 % (2772930)Instructions burned: 131 (million)
% 1.10/0.41 % (2772938)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3020903973:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.10/0.41 % Exception at run slice level
% 1.10/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.10/0.41 % (2772919)Instruction limit reached!
% 1.10/0.41 % (2772919)------------------------------
% 1.10/0.41 % (2772919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.41 % (2772919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.41 % (2772919)CaDiCaL version: 2.1.3
% 1.10/0.41 % (2772919)Termination reason: Instruction limit
% 1.10/0.41 % (2772919)Termination phase: Saturation
% 1.10/0.41 % (2772919)Time elapsed: 0.115 s
% 1.10/0.41 % (2772919)Peak memory usage: 12 MB
% 1.10/0.41 % (2772919)Instructions burned: 132 (million)
% 1.10/0.41 % (2772915) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2772909-2772915"...
% 1.10/0.41 % (2772915)...printing done.
% 1.10/0.41 % (2772915)Refutation found. Thanks to Tanya!
% 1.10/0.41 % SZS status Theorem for theBenchmark
% 1.10/0.41 % SZS output start Proof for theBenchmark
% 1.10/0.41 thf(type_def_5, type, a: $tType).
% 1.10/0.41 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 1.10/0.41 thf(func_def_1, type, sK0: (a > a > a)).
% 1.10/0.41 thf(func_def_2, type, sK1: (a > a > a)).
% 1.10/0.41 thf(func_def_3, type, sK2: a).
% 1.10/0.41 thf(func_def_4, type, sK3: a).
% 1.10/0.41 thf(func_def_5, type, sK4: a).
% 1.10/0.41 thf(func_def_6, type, sK5: a).
% 1.10/0.41 thf(func_def_7, type, sK6: a).
% 1.10/0.41 thf(func_def_8, type, sK7: (a > a)).
% 1.10/0.41 thf(f1,conjecture,(
% 1.10/0.41 ! [X0 : (a > a > a),X1 : (a > a > a),X2 : a,X3 : a] : ((! [X4 : a] : ? [X5 : a] : ((((X1 @ X4 @ X5)) = X3) & (((X0 @ X4 @ X5)) = X2)) & ! [X4 : a] : (((X0 @ X3 @ X4)) = X4) & ! [X4 : a] : (((X1 @ X3 @ X4)) = X3) & ! [X4 : a] : (((X0 @ X2 @ X4)) = X2) & ! [X4 : a] : (((X1 @ X2 @ X4)) = X4) & ! [X4 : a,X5 : a,X6 : a] : (((X0 @ X4 @ (X1 @ X5 @ X6))) = ((X1 @ (X0 @ X4 @ X5) @ (X0 @ X4 @ X6)))) & ! [X4 : a,X5 : a,X6 : a] : (((X1 @ X4 @ (X0 @ X5 @ X6))) = ((X0 @ (X1 @ X4 @ X5) @ (X1 @ X4 @ X6)))) & ! [X4 : a,X5 : a] : (((X1 @ (X0 @ X4 @ X5) @ X5)) = X5) & ! [X4 : a,X5 : a] : (((X0 @ (X1 @ X4 @ X5) @ X5)) = X5) & ! [X4 : a,X5 : a] : (((X1 @ X4 @ X5)) = ((X1 @ X5 @ X4))) & ! [X4 : a,X5 : a] : (((X0 @ X4 @ X5)) = ((X0 @ X5 @ X4))) & ! [X4 : a,X5 : a,X6 : a] : (((X1 @ (X1 @ X4 @ X5) @ X6)) = ((X1 @ X4 @ (X1 @ X5 @ X6)))) & ! [X4 : a,X5 : a,X6 : a] : (((X0 @ (X0 @ X4 @ X5) @ X6)) = ((X0 @ X4 @ (X0 @ X5 @ X6)))) & ! [X4 : a] : (((X1 @ X4 @ X4)) = X4) & ! [X4 : a] : (((X0 @ X4 @ X4)) = X4)) => ! [X4 : a,X5 : a,X6 : a] : (((((X1 @ X4 @ X6)) = X3) & (((X0 @ X4 @ X6)) = X2) & (((X1 @ X4 @ X5)) = X3) & (((X0 @ X4 @ X5)) = X2)) => (X5 = X6)))),
% 1.10/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCD_LATTICE_THM_pme)).
% 1.10/0.41 thf(f2,negated_conjecture,(
% 1.10/0.41 ~ ! [X0 : (a > a > a),X1 : (a > a > a),X2 : a,X3 : a] : ((! [X4 : a] : ? [X5 : a] : ((((X1 @ X4 @ X5)) = X3) & (((X0 @ X4 @ X5)) = X2)) & ! [X4 : a] : (((X0 @ X3 @ X4)) = X4) & ! [X4 : a] : (((X1 @ X3 @ X4)) = X3) & ! [X4 : a] : (((X0 @ X2 @ X4)) = X2) & ! [X4 : a] : (((X1 @ X2 @ X4)) = X4) & ! [X4 : a,X5 : a,X6 : a] : (((X0 @ X4 @ (X1 @ X5 @ X6))) = ((X1 @ (X0 @ X4 @ X5) @ (X0 @ X4 @ X6)))) & ! [X4 : a,X5 : a,X6 : a] : (((X1 @ X4 @ (X0 @ X5 @ X6))) = ((X0 @ (X1 @ X4 @ X5) @ (X1 @ X4 @ X6)))) & ! [X4 : a,X5 : a] : (((X1 @ (X0 @ X4 @ X5) @ X5)) = X5) & ! [X4 : a,X5 : a] : (((X0 @ (X1 @ X4 @ X5) @ X5)) = X5) & ! [X4 : a,X5 : a] : (((X1 @ X4 @ X5)) = ((X1 @ X5 @ X4))) & ! [X4 : a,X5 : a] : (((X0 @ X4 @ X5)) = ((X0 @ X5 @ X4))) & ! [X4 : a,X5 : a,X6 : a] : (((X1 @ (X1 @ X4 @ X5) @ X6)) = ((X1 @ X4 @ (X1 @ X5 @ X6)))) & ! [X4 : a,X5 : a,X6 : a] : (((X0 @ (X0 @ X4 @ X5) @ X6)) = ((X0 @ X4 @ (X0 @ X5 @ X6)))) & ! [X4 : a] : (((X1 @ X4 @ X4)) = X4) & ! [X4 : a] : (((X0 @ X4 @ X4)) = X4)) => ! [X4 : a,X5 : a,X6 : a] : (((((X1 @ X4 @ X6)) = X3) & (((X0 @ X4 @ X6)) = X2) & (((X1 @ X4 @ X5)) = X3) & (((X0 @ X4 @ X5)) = X2)) => (X5 = X6)))),
% 1.10/0.41 inference(negated_conjecture,[status(cth)],[f1])).
% 1.10/0.41 thf(f3,plain,(
% 1.10/0.41 ~ ! [X0 : (a > a > a),X1 : (a > a > a),X2 : a,X3 : a] : ((! [X4 : a] : ? [X5 : a] : ((((X1 @ X4 @ X5)) = X3) & (((X0 @ X4 @ X5)) = X2)) & ! [X6 : a] : (((X0 @ X3 @ X6)) = X6) & ! [X7 : a] : (((X1 @ X3 @ X7)) = X3) & ! [X8 : a] : (((X0 @ X2 @ X8)) = X2) & ! [X9 : a] : (((X1 @ X2 @ X9)) = X9) & ! [X10 : a,X11 : a,X12 : a] : (((X0 @ X10 @ (X1 @ X11 @ X12))) = ((X1 @ (X0 @ X10 @ X11) @ (X0 @ X10 @ X12)))) & ! [X13 : a,X14 : a,X15 : a] : (((X1 @ X13 @ (X0 @ X14 @ X15))) = ((X0 @ (X1 @ X13 @ X14) @ (X1 @ X13 @ X15)))) & ! [X16 : a,X17 : a] : (((X1 @ (X0 @ X16 @ X17) @ X17)) = X17) & ! [X18 : a,X19 : a] : (((X0 @ (X1 @ X18 @ X19) @ X19)) = X19) & ! [X20 : a,X21 : a] : (((X1 @ X20 @ X21)) = ((X1 @ X21 @ X20))) & ! [X22 : a,X23 : a] : (((X0 @ X22 @ X23)) = ((X0 @ X23 @ X22))) & ! [X24 : a,X25 : a,X26 : a] : (((X1 @ (X1 @ X24 @ X25) @ X26)) = ((X1 @ X24 @ (X1 @ X25 @ X26)))) & ! [X27 : a,X28 : a,X29 : a] : (((X0 @ (X0 @ X27 @ X28) @ X29)) = ((X0 @ X27 @ (X0 @ X28 @ X29)))) & ! [X30 : a] : (((X1 @ X30 @ X30)) = X30) & ! [X31 : a] : (((X0 @ X31 @ X31)) = X31)) => ! [X32 : a,X33 : a,X34 : a] : (((((X1 @ X32 @ X34)) = X3) & (((X0 @ X32 @ X34)) = X2) & (((X1 @ X32 @ X33)) = X3) & (((X0 @ X32 @ X33)) = X2)) => (X33 = X34)))),
% 1.10/0.41 inference(rectify,[],[f2])).
% 1.10/0.41 thf(f4,plain,(
% 1.10/0.41 ? [X0 : (a > a > a),X1 : (a > a > a),X2 : a,X3 : a] : (? [X32 : a,X33 : a,X34 : a] : ((X33 != X34) & ((((X1 @ X32 @ X34)) = X3) & (((X0 @ X32 @ X34)) = X2) & (((X1 @ X32 @ X33)) = X3) & (((X0 @ X32 @ X33)) = X2))) & (! [X4 : a] : ? [X5 : a] : ((((X1 @ X4 @ X5)) = X3) & (((X0 @ X4 @ X5)) = X2)) & ! [X6 : a] : (((X0 @ X3 @ X6)) = X6) & ! [X7 : a] : (((X1 @ X3 @ X7)) = X3) & ! [X8 : a] : (((X0 @ X2 @ X8)) = X2) & ! [X9 : a] : (((X1 @ X2 @ X9)) = X9) & ! [X10 : a,X11 : a,X12 : a] : (((X0 @ X10 @ (X1 @ X11 @ X12))) = ((X1 @ (X0 @ X10 @ X11) @ (X0 @ X10 @ X12)))) & ! [X13 : a,X14 : a,X15 : a] : (((X1 @ X13 @ (X0 @ X14 @ X15))) = ((X0 @ (X1 @ X13 @ X14) @ (X1 @ X13 @ X15)))) & ! [X16 : a,X17 : a] : (((X1 @ (X0 @ X16 @ X17) @ X17)) = X17) & ! [X18 : a,X19 : a] : (((X0 @ (X1 @ X18 @ X19) @ X19)) = X19) & ! [X20 : a,X21 : a] : (((X1 @ X20 @ X21)) = ((X1 @ X21 @ X20))) & ! [X22 : a,X23 : a] : (((X0 @ X22 @ X23)) = ((X0 @ X23 @ X22))) & ! [X24 : a,X25 : a,X26 : a] : (((X1 @ (X1 @ X24 @ X25) @ X26)) = ((X1 @ X24 @ (X1 @ X25 @ X26)))) & ! [X27 : a,X28 : a,X29 : a] : (((X0 @ (X0 @ X27 @ X28) @ X29)) = ((X0 @ X27 @ (X0 @ X28 @ X29)))) & ! [X30 : a] : (((X1 @ X30 @ X30)) = X30) & ! [X31 : a] : (((X0 @ X31 @ X31)) = X31)))),
% 1.10/0.41 inference(ennf_transformation,[],[f3])).
% 1.10/0.41 thf(f5,plain,(
% 1.10/0.41 ? [X0 : (a > a > a),X1 : (a > a > a),X2 : a,X3 : a] : (? [X32 : a,X33 : a,X34 : a] : ((X33 != X34) & (((X1 @ X32 @ X34)) = X3) & (((X0 @ X32 @ X34)) = X2) & (((X1 @ X32 @ X33)) = X3) & (((X0 @ X32 @ X33)) = X2)) & ! [X4 : a] : ? [X5 : a] : ((((X1 @ X4 @ X5)) = X3) & (((X0 @ X4 @ X5)) = X2)) & ! [X6 : a] : (((X0 @ X3 @ X6)) = X6) & ! [X7 : a] : (((X1 @ X3 @ X7)) = X3) & ! [X8 : a] : (((X0 @ X2 @ X8)) = X2) & ! [X9 : a] : (((X1 @ X2 @ X9)) = X9) & ! [X10 : a,X11 : a,X12 : a] : (((X0 @ X10 @ (X1 @ X11 @ X12))) = ((X1 @ (X0 @ X10 @ X11) @ (X0 @ X10 @ X12)))) & ! [X13 : a,X14 : a,X15 : a] : (((X1 @ X13 @ (X0 @ X14 @ X15))) = ((X0 @ (X1 @ X13 @ X14) @ (X1 @ X13 @ X15)))) & ! [X16 : a,X17 : a] : (((X1 @ (X0 @ X16 @ X17) @ X17)) = X17) & ! [X18 : a,X19 : a] : (((X0 @ (X1 @ X18 @ X19) @ X19)) = X19) & ! [X20 : a,X21 : a] : (((X1 @ X20 @ X21)) = ((X1 @ X21 @ X20))) & ! [X22 : a,X23 : a] : (((X0 @ X22 @ X23)) = ((X0 @ X23 @ X22))) & ! [X24 : a,X25 : a,X26 : a] : (((X1 @ (X1 @ X24 @ X25) @ X26)) = ((X1 @ X24 @ (X1 @ X25 @ X26)))) & ! [X27 : a,X28 : a,X29 : a] : (((X0 @ (X0 @ X27 @ X28) @ X29)) = ((X0 @ X27 @ (X0 @ X28 @ X29)))) & ! [X30 : a] : (((X1 @ X30 @ X30)) = X30) & ! [X31 : a] : (((X0 @ X31 @ X31)) = X31))),
% 1.10/0.41 inference(flattening,[],[f4])).
% 1.10/0.41 thf(f6,plain,(
% 1.10/0.41 ? [X0 : (a > a > a),X1 : (a > a > a),X2 : a,X3 : a] : (? [X4 : a,X5 : a,X6 : a] : ((X5 != X6) & (((X1 @ X4 @ X6)) = X3) & (((X0 @ X4 @ X6)) = X2) & (((X1 @ X4 @ X5)) = X3) & (((X0 @ X4 @ X5)) = X2)) & ! [X7 : a] : ? [X8 : a] : ((((X1 @ X7 @ X8)) = X3) & (((X0 @ X7 @ X8)) = X2)) & ! [X9 : a] : (((X0 @ X3 @ X9)) = X9) & ! [X10 : a] : (((X1 @ X3 @ X10)) = X3) & ! [X11 : a] : (((X0 @ X2 @ X11)) = X2) & ! [X12 : a] : (((X1 @ X2 @ X12)) = X12) & ! [X13 : a,X14 : a,X15 : a] : (((X0 @ X13 @ (X1 @ X14 @ X15))) = ((X1 @ (X0 @ X13 @ X14) @ (X0 @ X13 @ X15)))) & ! [X16 : a,X17 : a,X18 : a] : (((X1 @ X16 @ (X0 @ X17 @ X18))) = ((X0 @ (X1 @ X16 @ X17) @ (X1 @ X16 @ X18)))) & ! [X19 : a,X20 : a] : (((X1 @ (X0 @ X19 @ X20) @ X20)) = X20) & ! [X21 : a,X22 : a] : (((X0 @ (X1 @ X21 @ X22) @ X22)) = X22) & ! [X23 : a,X24 : a] : (((X1 @ X23 @ X24)) = ((X1 @ X24 @ X23))) & ! [X25 : a,X26 : a] : (((X0 @ X25 @ X26)) = ((X0 @ X26 @ X25))) & ! [X27 : a,X28 : a,X29 : a] : (((X1 @ (X1 @ X27 @ X28) @ X29)) = ((X1 @ X27 @ (X1 @ X28 @ X29)))) & ! [X30 : a,X31 : a,X32 : a] : (((X0 @ (X0 @ X30 @ X31) @ X32)) = ((X0 @ X30 @ (X0 @ X31 @ X32)))) & ! [X33 : a] : (((X1 @ X33 @ X33)) = X33) & ! [X34 : a] : (((X0 @ X34 @ X34)) = X34))),
% 1.10/0.41 inference(rectify,[],[f5])).
% 1.10/0.41 thf(f7,plain,(
% 1.10/0.41 ((sK5 != sK6) & (sK3 = ((sK1 @ sK4 @ sK6))) & (sK2 = ((sK0 @ sK4 @ sK6))) & (sK3 = ((sK1 @ sK4 @ sK5))) & (sK2 = ((sK0 @ sK4 @ sK5)))) & ! [X7 : a] : ((sK3 = ((sK1 @ X7 @ (sK7 @ X7)))) & (sK2 = ((sK0 @ X7 @ (sK7 @ X7))))) & ! [X9 : a] : (((sK0 @ sK3 @ X9)) = X9) & ! [X10 : a] : (sK3 = ((sK1 @ sK3 @ X10))) & ! [X11 : a] : (sK2 = ((sK0 @ sK2 @ X11))) & ! [X12 : a] : (((sK1 @ sK2 @ X12)) = X12) & ! [X13 : a,X14 : a,X15 : a] : (((sK0 @ X13 @ (sK1 @ X14 @ X15))) = ((sK1 @ (sK0 @ X13 @ X14) @ (sK0 @ X13 @ X15)))) & ! [X16 : a,X17 : a,X18 : a] : (((sK1 @ X16 @ (sK0 @ X17 @ X18))) = ((sK0 @ (sK1 @ X16 @ X17) @ (sK1 @ X16 @ X18)))) & ! [X19 : a,X20 : a] : (((sK1 @ (sK0 @ X19 @ X20) @ X20)) = X20) & ! [X21 : a,X22 : a] : (((sK0 @ (sK1 @ X21 @ X22) @ X22)) = X22) & ! [X23 : a,X24 : a] : (((sK1 @ X23 @ X24)) = ((sK1 @ X24 @ X23))) & ! [X25 : a,X26 : a] : (((sK0 @ X25 @ X26)) = ((sK0 @ X26 @ X25))) & ! [X27 : a,X28 : a,X29 : a] : (((sK1 @ (sK1 @ X27 @ X28) @ X29)) = ((sK1 @ X27 @ (sK1 @ X28 @ X29)))) & ! [X30 : a,X31 : a,X32 : a] : (((sK0 @ (sK0 @ X30 @ X31) @ X32)) = ((sK0 @ X30 @ (sK0 @ X31 @ X32)))) & ! [X33 : a] : (((sK1 @ X33 @ X33)) = X33) & ! [X34 : a] : (((sK0 @ X34 @ X34)) = X34)),
% 1.10/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X8,sK7 @ X7)],[f6])).
% 1.10/0.41 thf(f12,plain,(
% 1.10/0.41 ( ! [X26 : a,X25 : a] : ((((sK0 @ X25 @ X26)) = ((sK0 @ X26 @ X25)))) )),
% 1.10/0.41 inference(cnf_transformation,[],[f7])).
% 1.10/0.41 thf(f13,plain,(
% 1.10/0.41 ( ! [X24 : a,X23 : a] : ((((sK1 @ X23 @ X24)) = ((sK1 @ X24 @ X23)))) )),
% 1.10/0.41 inference(cnf_transformation,[],[f7])).
% 1.10/0.41 thf(f15,plain,(
% 1.10/0.41 ( ! [X19 : a,X20 : a] : ((((sK1 @ (sK0 @ X19 @ X20) @ X20)) = X20)) )),
% 1.10/0.41 inference(cnf_transformation,[],[f7])).
% 1.10/0.41 thf(f16,plain,(
% 1.10/0.41 ( ! [X18 : a,X16 : a,X17 : a] : ((((sK1 @ X16 @ (sK0 @ X17 @ X18))) = ((sK0 @ (sK1 @ X16 @ X17) @ (sK1 @ X16 @ X18))))) )),
% 1.10/0.41 inference(cnf_transformation,[],[f7])).
% 1.10/0.41 thf(f17,plain,(
% 1.10/0.41 ( ! [X14 : a,X15 : a,X13 : a] : ((((sK0 @ X13 @ (sK1 @ X14 @ X15))) = ((sK1 @ (sK0 @ X13 @ X14) @ (sK0 @ X13 @ X15))))) )),
% 1.10/0.41 inference(cnf_transformation,[],[f7])).
% 1.10/0.41 thf(f18,plain,(
% 1.10/0.41 ( ! [X12 : a] : ((((sK1 @ sK2 @ X12)) = X12)) )),
% 1.10/0.41 inference(cnf_transformation,[],[f7])).
% 1.10/0.41 thf(f21,plain,(
% 1.10/0.41 ( ! [X9 : a] : ((((sK0 @ sK3 @ X9)) = X9)) )),
% 1.10/0.41 inference(cnf_transformation,[],[f7])).
% 1.10/0.41 thf(f22,plain,(
% 1.10/0.41 ( ! [X7 : a] : ((sK2 = ((sK0 @ X7 @ (sK7 @ X7))))) )),
% 1.10/0.41 inference(cnf_transformation,[],[f7])).
% 1.10/0.41 thf(f23,plain,(
% 1.10/0.41 ( ! [X7 : a] : ((sK3 = ((sK1 @ X7 @ (sK7 @ X7))))) )),
% 1.10/0.41 inference(cnf_transformation,[],[f7])).
% 1.10/0.41 thf(f24,plain,(
% 1.10/0.41 (sK2 = ((sK0 @ sK4 @ sK5)))),
% 1.10/0.41 inference(cnf_transformation,[],[f7])).
% 1.10/0.41 thf(f25,plain,(
% 1.10/0.41 (sK3 = ((sK1 @ sK4 @ sK5)))),
% 1.10/0.41 inference(cnf_transformation,[],[f7])).
% 1.10/0.41 thf(f26,plain,(
% 1.10/0.41 (sK2 = ((sK0 @ sK4 @ sK6)))),
% 1.10/0.41 inference(cnf_transformation,[],[f7])).
% 1.10/0.41 thf(f27,plain,(
% 1.10/0.41 (sK3 = ((sK1 @ sK4 @ sK6)))),
% 1.10/0.41 inference(cnf_transformation,[],[f7])).
% 1.10/0.41 thf(f28,plain,(
% 1.10/0.41 (sK5 != sK6)),
% 1.10/0.41 inference(cnf_transformation,[],[f7])).
% 1.10/0.41 thf(f36,plain,(
% 1.10/0.41 ( ! [X0 : a] : ((((sK0 @ X0 @ sK3)) = X0)) )),
% 1.10/0.41 inference(constrained_superposition,[],[f12,f21])).
% 1.10/0.41 thf(f43,plain,(
% 1.10/0.41 ( ! [X0 : a] : ((((sK1 @ X0 @ sK2)) = X0)) )),
% 1.10/0.41 inference(constrained_superposition,[],[f13,f18])).
% 1.10/0.41 thf(f167,plain,(
% 1.10/0.41 ( ! [X0 : a,X1 : a] : ((((sK1 @ X0 @ (sK0 @ (sK7 @ X0) @ X1))) = ((sK0 @ sK3 @ (sK1 @ X0 @ X1))))) )),
% 1.10/0.41 inference(constrained_superposition,[],[f16,f23])).
% 1.10/0.41 thf(f168,plain,(
% 1.10/0.41 ( ! [X0 : a] : ((((sK1 @ sK4 @ (sK0 @ sK5 @ X0))) = ((sK0 @ sK3 @ (sK1 @ sK4 @ X0))))) )),
% 1.10/0.41 inference(constrained_superposition,[],[f16,f25])).
% 1.10/0.41 thf(f169,plain,(
% 1.10/0.41 ( ! [X0 : a] : ((((sK0 @ sK3 @ (sK1 @ sK4 @ X0))) = ((sK1 @ sK4 @ (sK0 @ sK6 @ X0))))) )),
% 1.10/0.41 inference(constrained_superposition,[],[f16,f27])).
% 1.10/0.41 thf(f182,plain,(
% 1.10/0.41 ( ! [X0 : a] : ((((sK1 @ sK4 @ X0)) = ((sK1 @ sK4 @ (sK0 @ sK6 @ X0))))) )),
% 1.10/0.41 inference(forward_demodulation,[],[f169,f21])).
% 1.10/0.41 thf(f183,plain,(
% 1.10/0.41 ( ! [X0 : a] : ((((sK1 @ sK4 @ X0)) = ((sK1 @ sK4 @ (sK0 @ sK5 @ X0))))) )),
% 1.10/0.41 inference(forward_demodulation,[],[f168,f21])).
% 1.10/0.41 thf(f184,plain,(
% 1.10/0.41 ( ! [X0 : a,X1 : a] : ((((sK1 @ X0 @ X1)) = ((sK1 @ X0 @ (sK0 @ (sK7 @ X0) @ X1))))) )),
% 1.10/0.41 inference(forward_demodulation,[],[f167,f21])).
% 1.10/0.41 thf(f224,plain,(
% 1.10/0.41 ( ! [X0 : a,X1 : a] : ((((sK1 @ sK2 @ (sK0 @ X0 @ X1))) = ((sK0 @ X0 @ (sK1 @ (sK7 @ X0) @ X1))))) )),
% 1.10/0.41 inference(constrained_superposition,[],[f17,f22])).
% 1.10/0.41 thf(f228,plain,(
% 1.10/0.41 ( ! [X0 : a] : ((((sK0 @ sK4 @ (sK1 @ sK5 @ X0))) = ((sK1 @ sK2 @ (sK0 @ sK4 @ X0))))) )),
% 1.10/0.41 inference(constrained_superposition,[],[f17,f24])).
% 1.10/0.41 thf(f229,plain,(
% 1.10/0.41 ( ! [X0 : a] : ((((sK1 @ sK2 @ (sK0 @ sK4 @ X0))) = ((sK0 @ sK4 @ (sK1 @ sK6 @ X0))))) )),
% 1.10/0.41 inference(constrained_superposition,[],[f17,f26])).
% 1.10/0.41 thf(f245,plain,(
% 1.10/0.41 ( ! [X0 : a] : ((((sK0 @ sK4 @ X0)) = ((sK0 @ sK4 @ (sK1 @ sK6 @ X0))))) )),
% 1.10/0.41 inference(forward_demodulation,[],[f229,f18])).
% 1.10/0.41 thf(f246,plain,(
% 1.10/0.41 ( ! [X0 : a] : ((((sK0 @ sK4 @ X0)) = ((sK0 @ sK4 @ (sK1 @ sK5 @ X0))))) )),
% 1.10/0.41 inference(forward_demodulation,[],[f228,f18])).
% 1.10/0.41 thf(f250,plain,(
% 1.10/0.41 ( ! [X0 : a,X1 : a] : ((((sK0 @ X0 @ X1)) = ((sK0 @ X0 @ (sK1 @ (sK7 @ X0) @ X1))))) )),
% 1.10/0.41 inference(forward_demodulation,[],[f224,f18])).
% 1.10/0.41 thf(f817,plain,(
% 1.10/0.41 (((sK1 @ sK4 @ sK2)) = ((sK1 @ sK4 @ (sK7 @ sK6))))),
% 1.10/0.41 inference(constrained_superposition,[],[f182,f22])).
% 1.10/0.41 thf(f840,plain,(
% 1.10/0.41 (((sK1 @ sK2 @ sK4)) = ((sK1 @ sK4 @ (sK7 @ sK6))))),
% 1.10/0.41 inference(forward_demodulation,[],[f817,f13])).
% 1.10/0.41 thf(f844,plain,(
% 1.10/0.41 (sK4 = ((sK1 @ sK4 @ (sK7 @ sK6))))),
% 1.10/0.41 inference(forward_demodulation,[],[f840,f18])).
% 1.10/0.41 thf(f859,plain,(
% 1.10/0.41 (((sK1 @ sK4 @ sK2)) = ((sK1 @ sK4 @ (sK7 @ sK5))))),
% 1.10/0.41 inference(constrained_superposition,[],[f183,f22])).
% 1.10/0.41 thf(f882,plain,(
% 1.10/0.41 (((sK1 @ sK2 @ sK4)) = ((sK1 @ sK4 @ (sK7 @ sK5))))),
% 1.10/0.41 inference(forward_demodulation,[],[f859,f13])).
% 1.10/0.41 thf(f886,plain,(
% 1.10/0.41 (sK4 = ((sK1 @ sK4 @ (sK7 @ sK5))))),
% 1.10/0.41 inference(forward_demodulation,[],[f882,f18])).
% 1.10/0.41 thf(f955,plain,(
% 1.10/0.41 (((sK0 @ sK4 @ sK3)) = ((sK0 @ sK4 @ (sK7 @ sK6))))),
% 1.10/0.41 inference(constrained_superposition,[],[f245,f23])).
% 1.10/0.41 thf(f978,plain,(
% 1.10/0.41 (((sK0 @ sK3 @ sK4)) = ((sK0 @ sK4 @ (sK7 @ sK6))))),
% 1.10/0.41 inference(forward_demodulation,[],[f955,f12])).
% 1.10/0.41 thf(f982,plain,(
% 1.10/0.41 (sK4 = ((sK0 @ sK4 @ (sK7 @ sK6))))),
% 1.10/0.41 inference(forward_demodulation,[],[f978,f21])).
% 1.10/0.41 thf(f985,plain,(
% 1.10/0.41 (((sK0 @ sK4 @ sK3)) = ((sK0 @ sK4 @ (sK7 @ sK5))))),
% 1.10/0.41 inference(constrained_superposition,[],[f246,f23])).
% 1.10/0.41 thf(f1008,plain,(
% 1.10/0.41 (((sK0 @ sK3 @ sK4)) = ((sK0 @ sK4 @ (sK7 @ sK5))))),
% 1.10/0.41 inference(forward_demodulation,[],[f985,f12])).
% 1.10/0.41 thf(f1012,plain,(
% 1.10/0.41 (sK4 = ((sK0 @ sK4 @ (sK7 @ sK5))))),
% 1.10/0.41 inference(forward_demodulation,[],[f1008,f21])).
% 1.10/0.41 thf(f1026,plain,(
% 1.10/0.41 (((sK7 @ sK6)) = ((sK1 @ sK4 @ (sK7 @ sK6))))),
% 1.10/0.41 inference(constrained_superposition,[],[f15,f982])).
% 1.10/0.41 thf(f1036,plain,(
% 1.10/0.41 (sK4 = ((sK7 @ sK6)))),
% 1.10/0.41 inference(forward_demodulation,[],[f1026,f844])).
% 1.10/0.41 thf(f1231,plain,(
% 1.10/0.41 ( ! [X0 : a] : ((((sK1 @ X0 @ sK2)) = ((sK1 @ X0 @ (sK7 @ (sK7 @ X0)))))) )),
% 1.10/0.41 inference(constrained_superposition,[],[f184,f22])).
% 1.10/0.41 thf(f1283,plain,(
% 1.10/0.41 ( ! [X0 : a] : ((((sK1 @ X0 @ (sK7 @ (sK7 @ X0)))) = X0)) )),
% 1.10/0.41 inference(forward_demodulation,[],[f1231,f43])).
% 1.10/0.41 thf(f1409,plain,(
% 1.10/0.41 (((sK7 @ sK5)) = ((sK1 @ sK4 @ (sK7 @ sK5))))),
% 1.10/0.41 inference(constrained_superposition,[],[f15,f1012])).
% 1.10/0.41 thf(f1421,plain,(
% 1.10/0.41 (sK4 = ((sK7 @ sK5)))),
% 1.10/0.41 inference(forward_demodulation,[],[f1409,f886])).
% 1.10/0.41 thf(f1428,plain,(
% 1.10/0.41 ( ! [X0 : a] : ((((sK0 @ X0 @ sK3)) = ((sK0 @ X0 @ (sK7 @ (sK7 @ X0)))))) )),
% 1.10/0.41 inference(constrained_superposition,[],[f250,f23])).
% 1.10/0.41 thf(f1478,plain,(
% 1.10/0.41 ( ! [X0 : a] : ((((sK0 @ X0 @ (sK7 @ (sK7 @ X0)))) = X0)) )),
% 1.10/0.41 inference(forward_demodulation,[],[f1428,f36])).
% 1.10/0.41 thf(f3104,plain,(
% 1.10/0.41 ( ! [X0 : a] : ((((sK7 @ (sK7 @ X0))) = ((sK1 @ X0 @ (sK7 @ (sK7 @ X0)))))) )),
% 1.10/0.41 inference(constrained_superposition,[],[f15,f1478])).
% 1.10/0.41 thf(f3128,plain,(
% 1.10/0.41 ( ! [X0 : a] : ((((sK7 @ (sK7 @ X0))) = X0)) )),
% 1.10/0.41 inference(forward_demodulation,[],[f3104,f1283])).
% 1.10/0.41 thf(f3142,plain,(
% 1.10/0.41 (sK5 = ((sK7 @ sK4)))),
% 1.10/0.41 inference(constrained_superposition,[],[f3128,f1421])).
% 1.10/0.41 thf(f3143,plain,(
% 1.10/0.41 (sK6 = ((sK7 @ sK4)))),
% 1.10/0.41 inference(constrained_superposition,[],[f3128,f1036])).
% 1.10/0.41 thf(f3174,plain,(
% 1.10/0.41 (sK5 = sK6)),
% 1.10/0.41 inference(forward_demodulation,[],[f3143,f3142])).
% 1.10/0.41 thf(f3175,plain,(
% 1.10/0.41 $false),
% 1.10/0.41 inference(forward_subsumption_resolution,[],[f3174,f28])).
% 1.10/0.41 % SZS output end Proof for theBenchmark
% 1.10/0.41 % (2772915)------------------------------
% 1.10/0.41 % (2772915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.41 % (2772915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.41 % (2772915)CaDiCaL version: 2.1.3
% 1.10/0.41 % (2772915)Termination reason: Refutation
% 1.10/0.41 % (2772915)Time elapsed: 0.142 s
% 1.10/0.41 % (2772915)Peak memory usage: 13 MB
% 1.10/0.41 % (2772915)Instructions burned: 295 (million)
% 1.10/0.41 % (2772909)Success in time 0.181 s
% 1.10/0.41 % Vampire exiting
%------------------------------------------------------------------------------